2024-03-29T11:29:50Z
https://wala.vru.ac.ir/?_action=export&rf=summon&issue=33380
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2021
8
1
A note on zero Lie product determined nest algebras as Banach algebras
Hoger
Ghahramani
Kamal
Fallahi
Wania
Khodakarami
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.
Zero Lie product determined Banach algebra
nest algebra
weakly amenable Banach algebra
2021
07
01
1
6
https://wala.vru.ac.ir/article_245222_bba88ea53ec7d84e8f04748e3bd83bb6.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2021
8
1
On the frames by multiplication and irregular frames of translates on LCA groups
N.S.
Seyedi
M.
Mortazavizadeh
R. A.
Kamyabi Gol
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.
locally compact abelian group
frame by multiplication
irregular frame of translates
2021
07
01
7
16
https://wala.vru.ac.ir/article_245223_ac1d03935a9178a6ee5d0304f9408375.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2021
8
1
Some inequalities related to 4-convex functions
Shiva
Mohtashami
Abbas
Salemi
Mohammad
Soleymani
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 $\mathbb{R}_4$.
Majorization
4-convex function
inequalities
divided difference
2021
07
01
17
26
https://wala.vru.ac.ir/article_245224_c97da2b38322d1a32bbb3d14e074d660.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2021
8
1
Linear Preservers of Doubly stochastic matrices and permutation matrices from $M_m$ to $M_n$
H.
Baharlooei
M.
Chaichi Raghimi
A.
Bayati Eshkaftaki
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.
Doubly stochastic matrix
Linear manifold
Generalized doubly stochastic matrices
(Strong) Preserver
2021
07
01
27
36
https://wala.vru.ac.ir/article_245233_3425f1372b4867d9631afcbad5efeb7b.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2021
8
1
On $n$-weak biamenability of Banach algebras
Sedigheh
Barootkoob
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 $n$.
biderivation
inner biderivation
$n$-weak biamenability
2021
07
01
37
47
https://wala.vru.ac.ir/article_245234_cfbaa6fffcfebf86e5930fc538e10a5c.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2021
8
1
On I-biflat and I-biprojective Banach algebras
Amir
Sahami
Mehdi
Rostami
Shahab
Kalantari
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.
$I$-biflatness
$I$-biprojectivity
Banach algebra
2021
07
01
49
59
https://wala.vru.ac.ir/article_245235_cc24b6306c3845b11178cede6571704a.pdf
Wavelet and Linear Algebra
WALA
2383-1936
2383-1936
2021
8
1
Application Of Wavelets To Improve Cancer Diagnosis Model In High Dimensional Linguistic DNA Microarray Datasets
Nasibeh
Emami
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.
fuzzy numbers
linguistic data
diagnosis cancer
Wavelet decomposition
high dimensional data
2021
07
01
61
72
https://wala.vru.ac.ir/article_245236_2514a5d3c678f6b60b8e9cfd19a85ea9.pdf