ORIGINAL_ARTICLE
A note on zero Lie product determined nest algebras as Banach algebras
A Banach algebra $\A$ is said to be zero Lie product determined Banach algebra if for every continuous bilinear functional $\phi:\A \times \A\rightarrow \mathbb{C}$ the following holds: if $\phi(a,b)=0$ whenever $ab=ba$, then there exists some $\tau \in \A^*$ such that $\phi(a,b)=\tau(ab-ba)$ for all $a,b\in \A$. We show that any finite nest algebra over a complex Hilbert space is a zero Lie product determined Banach algebra.
https://wala.vru.ac.ir/article_245222_bba88ea53ec7d84e8f04748e3bd83bb6.pdf
2021-07-01
1
6
10.22072/wala.2020.130358.1293
Zero Lie product determined Banach algebra
nest algebra
weakly amenable Banach algebra
Hoger
Ghahramani
h.ghahramani@uok.ac.ir
1
Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran.
LEAD_AUTHOR
Kamal
Fallahi
fallahi1361@gmail.com
2
Department of Mathematics, Payam Noor University of Technology, P.O. Box 19395-3697, Tehran, Iran.
AUTHOR
Wania
Khodakarami
wania.khodakarami@gmail.com
3
Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran.
AUTHOR
[1] J. Alaminos, M. Bre$check{textrm{s}}$ar, J. Extremera, $check{textrm{S}}$. $check{textrm{S}}$penko and A.R. Villena, Commutators and square-zero elements in Banach algebras, Q. J. Math., 67 (2016), 1-13.
1
[2] J. Alaminos, M. Bre$check{textrm{s}}$ar, J. Extremera and A.R. Villena, Maps preserving zero products, Studia Math., 193 (2009), 131-159.
2
[3] J. Alaminos, M. Bre$check{textrm{s}}$ar, J. Extremera and A.R. Villena, newblock Zero Lie product determined Banach algebras, II, J. Math. Anal. Appl., 474 (2019), 1498-1511.
3
[4] J. Alaminos, M. Bre$check{textrm{s}}$ar, J. Extremera and A.R. Villena, Zero Lie product determined Banach algebras, Studia Math., 239 (2017), 189-199.
4
[5] M. Bre$check{textrm{s}}$ar, Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. R. Soc. Edinb., Sect. A, Math., 137 (2007), 9-21.
5
[6] M. Bre$check{textrm{s}}$ar, Finite dimensional zero product determined algebras are generated by idempotents, Expo. Math., 34 (2016), 130-143.
6
[7] M. Bre$check{textrm{s}}$ar, Functional identities and zero Lie product determined Banach algebras, Q. J. Math., 71 (2020), 649-665.
7
[8] M. Bre$check{textrm{s}}$ar, M. Gra$check{textrm{s}}$i$check{textrm{c}}$ and J. Sanchez, Zero product determined matrix algebras, Linear Algebra Appl., 430 (2009), 1486-1498.
8
[9] M. Bre$check{textrm{s}}$ar, Multiplication algebra and maps determined by zero products, Linear Multilinear Algebra, 60 (2012), 763-768.
9
[10] M. Bre$check{textrm{s}}$ar and P. $check{textrm{S}}$emrl, On bilinear maps on matrices with applications to commutativity preservers, J. Algebra, 301 (2006), 803-837.
10
[11] H.G. Dales, Banach Algebras and Automatic Continuity, London Mathematical Society Monographs, New Series, 24, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 2000.
11
[12] K.R. Davidson, Nest Algebras, Pitman Research Notes in Mathematics, 191, Longman, London, 1988.
12
[13] B.E. Forrest and L.W. Marcoux, Derivations of triangular Bnach algebras, Indiana Univ. Math. J., 45 (1996), 441-462.
13
[14]] B.E. Forrest and L.W. Marcoux, Weak amenability of triangular Banach algebras, Trans. Am. Math. Soc., 345 (2002), 1435-1452.
14
[15] H. Ghahramani, Zero product determined some nest algebras, Linear Algebra Appl., 438 (2013), 303-314.
15
[16] H. Ghahramani, Zero product determined triangular algebras, Linear Multilinear Algebra, 61 (2013), 741-757.
16
[17] M. Gra$check{textrm{s}}$i$check{textrm{c}}$, Zero product determined classical Lie algebras, Linear Multilinear Algebra, 58 (2010), 1007-1022.
17
[18] C. Pearcy and D. Topping, Sum of small numbers of idempotent, Mich. Math. J., 14 (1967), 453-465.
18
[19] D. Wang, X. Yu and Z. Chen, newblock A class of zero product determined Lie algebras, J. Algebra, 331 (2011), 145-151.
19
ORIGINAL_ARTICLE
On the frames by multiplication and irregular frames of translates on LCA groups
Let $X$ be a measure space and let $E$ be a measurable subset of $X$ with finite positive measure. In this paper, we investigate frame and Riesz basis properties of a family of functions multiplied by another measurable function in $L^2(E)$. Also, we study the equivalent conditions for a system of translates to be a Bessel family in $L^2(G)$ and to be a frame for $P_E$ (the space of the band limited functions). Finally, we study the properties of frames of translates that preserved by convolution.
https://wala.vru.ac.ir/article_245223_ac1d03935a9178a6ee5d0304f9408375.pdf
2021-07-01
7
16
10.22072/wala.2021.130732.1295
locally compact abelian group
frame by multiplication
irregular frame of translates
N.S.
Seyedi
na.seyedi@mail.um.ac.ir
1
Department of Pure Mathematics, Ferdowsi University of Mashhad, Iran.
AUTHOR
M.
Mortazavizadeh
mortazavizadeh@mail.um.ac.ir
2
Department of Pure Mathematics, Ferdowsi University of Mashhad, Iran.
AUTHOR
R. A.
Kamyabi Gol
kamyabi@um.ac.ir
3
Department of Pure Mathematics, Ferdowsi University of Mashhad, Iran.
LEAD_AUTHOR
[1] A. Aldroubi and K. Gr$ddot{text{o}}$chenig, Non-uniform sampling and reconstruction in shift-invariant spaces, SIAM Rev., 43 (2001), 585-620.
1
[2] P. Balazs, C. Cabrelli, S. Heineken and U. Molter, Frames by multiplication, Curr. Dev. Theory Appl. Wavelets, (2011), 165-186.
2
[3] J.J. Benedetto and O. Treiber, Wavelet Transforms and Time- Frequency Signal Analysis, chapter Wavelet frames: Multiresolution analysis and extension principle, Birkh$ddot{text{a}}$user, 2001.
3
[4] M. Bownik, The structure of shift-invariant subspaces of $L^2(mathbb{R}^n)$, J. Funct. Anal., 177(2) (2000), 282-309.
4
[5] P. Casazza, O. Christensen and N.J. Kalton, Frames of translates, Collect. Math., 1 (2001), 35-54.
5
[6] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhauser, 2015.
6
[7] R.J. Duffine and A.C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc., 72} (1952), 341-366.
7
[8] G.B. Folland, A Course in Abstract Harmonic Analysis, CRS Press, 1995.
8
[9] C. Heil, A Basis Theory Primer, Birkhauser, 2011.
9
[10] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, vol. 1, Springer-Verlag, 1963.
10
[11] R.A. Kamyabi Gol and R. Raisi Tousi, The structure of shift invariant spaces on locally compact abelian group, J. Math. Anal. Appl., 340 (2008), 219-225.
11
[12] N.S. Seyedi and R.A. Kamyabi Gol, On the frames of translates on locally compact abelian groups, Preperint.
12
ORIGINAL_ARTICLE
Some inequalities related to 4-convex functions
In this paper, we consider the class of 4-convex functions and we obtain some inequalities related to 4-convex functions. Moreover, for $k\leq n$, we present a majorization $\prec_k $ on $\mathbb{R}_n$ and we give some equivalent conditions for $\prec_4 $ on $\mathbb{R}_4$.
https://wala.vru.ac.ir/article_245224_c97da2b38322d1a32bbb3d14e074d660.pdf
2021-07-01
17
26
10.22072/wala.2021.130889.1296
Majorization
4-convex function
inequalities
divided difference
Shiva
Mohtashami
mohtashami@yahoo.com
1
Department of Mathematics, Islamic Azad University, Kerman branch, Kerman, Iran.
AUTHOR
Abbas
Salemi
salemi@uk.ac.ir
2
Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.
AUTHOR
Mohammad
Soleymani
m.soleymani@uk.ac.ir
3
Department of Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.
LEAD_AUTHOR
[1] G. Bennett, A p-free $ell^p$-inequality, J. Math. Inequal., 3(1) (2009), 155-159.
1
[2] G. Bennett, p-free $ell^p$-inequalities, Am. Math. Mon., 117(4) (2010), 334-351.
2
[3] P.S. Bullen, A criterion for n-convexity, Pac. J. Math., 36(1) (1971), 81-98.
3
[4] J.L. Coolidge, A Treatise on Algebraic Plane Curves, New York, 1959.
4
[5] G.H. Hardy, J.E. Littlewood and G. Polya, Inequalities, 2nd edition, Cambridge University Press, Cambridge, 1967.
5
[6] D.S. Marinescu and M. Monea, Some inequalities for convex and $3$-convex function with applications, Kragujevac J. Math., 39(1) (2015), 83-91.
6
[7] D.G. Mead, Newton's identities, Am. Math. Mon., 99(8) (1992), 749-751.
7
[8] L.M. Milne-Thomson, The calculus of Finite Differences, Macmillan, London, 1933.
8
ORIGINAL_ARTICLE
Linear Preservers of Doubly stochastic matrices and permutation matrices from $M_m$ to $M_n$
Chi-Kwang Li, Bit-Shun Tam and Nam-Kiu Tsing have obtained necessary and sufficient condition for a linear operator on linear space of generalized doubly stochastic matrices to be strong preserver of doubly stochastic matrices and permutation matrices. We show if a linear operator $T:M_m\rightarrow M_n$ is a (strong) preserver of doubly stochastic matrices, then $T$ is a (strong) preserver of the linear manifold of r-generalized doubly stochastic matrices and the linear space of generalized doubly stochastic matrices. Also we give necessary and sufficient condition for a linear operator $T:M_m\rightarrow M_n$ to be (strong) preserver of doubly stochastic matrices and permutation matrices.
https://wala.vru.ac.ir/article_245233_3425f1372b4867d9631afcbad5efeb7b.pdf
2021-07-01
27
36
10.22072/wala.2021.131790.1298
Doubly stochastic matrix
Linear manifold
Generalized doubly stochastic matrices
(Strong) Preserver
H.
Baharlooei
hamidbaharlooei14@gmail.com
1
Instietute of Advanced Studies, Payame Noor University, P.O. Box 19395- 3697, Tehran, Iran.
AUTHOR
M.
Chaichi Raghimi
chaichi@pnu.ac.ir
2
Department of Mathematic, Payame Noor University, P.O. Box 19395- 3697, Tehran, Iran.
LEAD_AUTHOR
A.
Bayati Eshkaftaki
bayati.ali@sku.ac.ir
3
Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, 88186-34141, Iran.
AUTHOR
[1] A. Douik and B. Hassibi, Manifold optimization over the set of doubly stochastic matrices, IEEE Trans. Signal Process., 67(22) (2019), 5761-5774.
1
[2] D. Hug and W. Weil, A Course on Convex Geometry, University of Karlsruhe 2011.
2
[3] C.K. Li, B.S. Tam and N.K. Tsing, Linear maps preserving permutation and stochastic matrices, Linear Algebra Appl., 341 (2002), 5-22.
3
[4] A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities, Theory of Majorization and Its Applications, 2nd ed., Springer, NewYork, 2011.
4
[5] B. Mourad, On lie theoretic approach to general doubly stochastic matrices and applications, Linear Multilinear Algebra, 52(2) (2013), 99-113.
5
[6] M. Murray, Some Notes on Differential Geometry, University of Adelaide July 20, 2009.
6
ORIGINAL_ARTICLE
On $n$-weak biamenability of Banach algebras
In this paper, the notion of $n$-weak biamenability of Banach algebras is introduced and for every $n\geq 3$, it is shown that $n$-weak biamenability of the second dual $A^{**}$ of a Banach algebra $A$ implies $n$-weak biamenability of $A$ and this is true for $n=1, 2$ under some mild conditions. As a concrete example, it is shown that for every abelian locally compact group $G$, $L^1(G)$ is $1$-weakly biamenable and $\ell^1(G)$ is $n$-weakly biamenable for every odd integer $n$.
https://wala.vru.ac.ir/article_245234_cfbaa6fffcfebf86e5930fc538e10a5c.pdf
2021-07-01
37
47
10.22072/wala.2020.135455.1300
biderivation
inner biderivation
$n$-weak biamenability
Sedigheh
Barootkoob
s.barutkub@ub.ac.ir
1
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord, Iran.
LEAD_AUTHOR
[1] A. Arens, The adjoint of a bilinear operation, Proc. Am. Math. Soc., 2 (1951), 839-848.
1
[2] S. Barootkoob, On biamenability of Banach algebras, Preprint, arXiv:2011.12653v1, 2020.
2
[3] S. Barootkoob and H.R. Ebrahimi Vishki, Lifting derivations and $n$-weak amenability of the second dual of Banach algebras, Bull. Aust. Math. Soc., 83 (2011), 122-129.
3
[4] D. Benkoviv{c}, Biderivations of triangular algebras, Linear Algebra Appl., 431 (2009), 1587-1602.
4
[5] M. Brev{s}ar, Commuting maps: A survey, Taiwanese J. Math., 8 (2004), 361-397.
5
[6] H.G. Dales, F. Ghahramani and N. Gr{o}nb{ae}k, Derivations into iterated duals of Banach algebras, Stud. Math., 128(1) (1998), 19-54.
6
[7] M. Despiv{c} and F. Ghahramani, Weak amenability of group algebras of locally compact groups, Can. Math. Bull., 37 (1994), 165-167.
7
[8] Y. Du and Y. Wang, Biderivations of generalized matrix algebras, Linear Algebra Appl., 438 (2013), 4483-4499.
8
[9] Y. Zhang, $2m$-weak amenability of group algebras, J. Math. Anal. Appl., 396 (2012), 412-416.
9
[10] Y. Zhang, Weak amenability of module extensions of Banach algebras, Trans. Am. Math. Soc., 354(10) (2002), 4131-4151.
10
ORIGINAL_ARTICLE
On I-biflat and I-biprojective Banach algebras
In this paper, we introduce new notions of $I$-biflatness and $I$-biprojectivity, for a Banach algebra $A$, where $I$ is a closed ideal of $A$. We show that $M(G)$ is $L^{1}(G)$-biprojective ($I$-biflat) if and only if $G$ is a compact group (an amenable group), respectively. Also, we show that, for a non-zero ideal $I$, if the Fourier algebra $A(G)$ is $I$-biprojective, then $G$ is a discrete group. Some examples are given to show the differences between these new notions and the classical ones.
https://wala.vru.ac.ir/article_245235_cc24b6306c3845b11178cede6571704a.pdf
2021-07-01
49
59
10.22072/wala.2021.141939.1311
$I$-biflatness
$I$-biprojectivity
Banach algebra
Amir
Sahami
a.sahami@ilam.ac.ir
1
Department of Mathematics Faculty of Basic Science, Ilam University, P.O. Box 69315-516 Ilam, Iran.
LEAD_AUTHOR
Mehdi
Rostami
mross@aut.ac.ir
2
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, 15914 Tehran, Iran.
AUTHOR
Shahab
Kalantari
shahab.kalantari@nit.ac.ir
3
Department of Basic Sciences, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran, Post Code:47148-71167.
AUTHOR
[1] H.G. Dales and R.J. Loy, Approximate amenability of semigroup algebras and Segal algebras, Diss. Math., 474 (2010), 1-58.
1
[2] J. Duncan and A.L.T. Paterson, Amenability for discrete convolution semigroup algebras, Math. Scand., 66 (1990), 141-146.
2
[3] F. Ghahramani and A.T. Lau, Multipliers and ideals in second conjugate algebras related to locally compact groups, J. Funct. Anal., 132 (1995), 170-191.
3
[4] F. Ghahramani, R.J. Loy and G.A. Willis, Amenability and weak amenability of second conjugate Banach algebras, Proc. Am. Math. Soc., 124 (1996), 1489-1497.
4
[5] A.Ya. Helemskii, Banach and Locally Convex Algebras, Oxford Univ.Press, Oxford, 1993.
5
[6] A.Ya. Helemskii, The Homology of Banach and Topological Algebras, Kluwer, Academic Press, Dordrecht, 1989.
6
[7] B.E. Johnson, Cohomology in Banach Algebras, Memoirs of the American Mathematical Society, 1972.
7
[8] A.R. Medghalchi and M.H. Sattari, Biflatness and biprojectivity of triangular Banach algebras, Bull. Iran. Math. Soc., 34 (2008), 115-120.
8
[9] R. Nasr Isfahani and S. Soltani Renani, Character contractibility of Banach algebras and homological properties of Banach modules, Stud. Math., 202(3) (2011), 205-225.
9
[10] V. Runde, Lectures on Amenability, Springer, New York, 2002.
10
[11] A. Sahami and A. Pourabbas, On $phi$-biflat and $phi$-biprojective Banach algebras, Bull. Belg. Math. Soc. Simon Stevin, 20(5) (2013), 789-801.
11
ORIGINAL_ARTICLE
Application Of Wavelets To Improve Cancer Diagnosis Model In High Dimensional Linguistic DNA Microarray Datasets
DNA microarray datasets suffer scaling and uncertainty problems. This paper develops a model that manages DNA microarray datasets challenges more precisely by using the advantages of Wavelet decomposition and fuzzy numbers. For this aim, the proposed method is utilized to classify linguistic DNA microarray datasets set, where datasets can be given as linguistic genes. Linguistic genes are represented by using triangular fuzzy numbers provided as LR (left-right) fuzzy numbers. Then the WABL method is applied as the defuzzification method. Also, a set of orthogonal wavelet detail coefficients based on wavelet decomposition at different levels is extracted to specify the localized genes of DNA microarray datasets. Three DNA microarray datasets are used to evaluate this method. The experiments are shown that the proposed model has better diagnostic accuracy than other methods.
https://wala.vru.ac.ir/article_245236_2514a5d3c678f6b60b8e9cfd19a85ea9.pdf
2021-07-01
61
72
10.22072/wala.2021.520825.1312
fuzzy numbers
linguistic data
diagnosis cancer
Wavelet decomposition
high dimensional data
Nasibeh
Emami
nasibeh.emami@kub.ac.ir
1
Department of computer science, faculty of basic sciences, kosar university of bojnord, bojnord, Iran.
LEAD_AUTHOR
[1] A. Alkuhlani, M. Nassef and I. Farag, Multistage feature selection approach for high-dimensional cancer data, Soft Comput., 21 (2017), 6895-6906.
1
[2] A. Grossmann and J. Morlet, Decomposition of hardy functions into square integrable wavelets of constant shape, SIAM J. Math. Anal., 15(4) (1984), 723-736.
2
[3] A.M.S Roque, C. Mate, j. Arroyo and A. Sarabia, Imlp: applying multi-layer perceptrons to interval-valued data. Neural processing letters, SIAM J. Math. Anal., 25 (2007), 157-169.
3
[4] D.S Huang and CH. Zheng, Independent component analysis-based penalized discriminant Method for tumor classification using gene expression data, Biostat. Bioinform. Biomath., 22(15) (2006) 1855-1862.
4
[5] E. Nasibov and A. Mert, On methods of defuzzification of parametrically represented fuzzy numbers, Autom. Control Comput. Sci., 41 (2007), 265-273.
5
[6] E. Nasibov, Aggregation of fuzzy information on the basis of decompositional representation, Cybern. Syst. Anal., 41(2), (2005), 309-318.
6
[7] L. Yang and Z. Xu, Feature extraction by pca and diagnosis of breast tumors using SVM with de-based parameter tuning, International Journal of Machine Learning and Cybernetics, 10 (2017), 591-601.
7
[8] L.A. Zadeh, The concept of linguistic variable and its application to approximate reasoning, Inf. Sci., 8(3) (1975), 199-249.
8
[9] Z.M. Hira and D.F. Gillies, A review of feature selection and feature extraction methods applied on microarray data, Advances in Bioinformatics, 2015(5) (2015), 1-13.
9
[10] R.E. Moore, R.B. Kearfott and M.J. Cloud, Introduction to Interval Analysis, Society for Industrial and Applied Mathematics Philadelphia, 2009.
10
[11] S. Sarbazi-azad, M. Saniee Abadeh and M.E. Mowlaei, Using data complexity measures and an evolutionary cultural algorithm for gene selection in microarray data, Soft computing letters, DOI:10.1016/j.socl.2020.100007, 2020.
11
[12] S. Tabakhi, A. Njafi. R. Ranjbar and P. Moradi, Gene selection for microarray data classification using a novel ant colony optimization, Neurocomputing, 168 (2015), 1024-1036.
12
[13] S.K Sava and E. Nasibov, A fuzzy id3 induction for linguistic data sets, International journal of intelligent systems, 33(4) (2018), 1-21.
13
[14] S.M Saqlainshah, F. Alishah, S.A Hussain and S. Batool, Support vector machines-based heart disease diagnosis using feature subset, wrapping selection and extraction methods, Comput. Electr. Eng., 84(10) (2020), DOI:10.1016/j.compeleceng.2020.106628.
14
[15] S.O.M kasha and M. A Akbarzadeh, A framework for short-term traffic flow forecasting using the combination of wavelet transformation and artificial neural networks, J. Intell. Transp. Syst., 23(1) (2019), 1-12.
15
[16] X. Zheng, W. Zhu, CH. Tang and M. Wang, Gene selection for microarray data classification via adaptive hypergraph embedded dictionary learning, Gene, 706 (2019), 188-200.
16
[17] Y. Liu, Wavelet feature extraction for high-dimensional microarray data, Neurocomputing, 72 (2009), 985-990.
17
[18] X. Wu and et al., Top 10 algorithms in data mining, Knowledge and Information Systems, 14 (2008), 1-37.
18
[19] J. Basavaiah and A.A. Anthony, Tomato Leaf Disease Classification using Multiple Feature Extraction Techniques, Wireless Personal Communications, 115 (2020), 633-651.
19