Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367120200801Excess of continuous $K$-$g$-frames and some other propertiesبیش از حد فریم K-g مداوم و برخی از خواص دیگر1113794210.22072/wala.2019.109025.1230ENElnaz Nobahar AlamdariDepartment of mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Islamic Republic of Iran.Mehrdad AzadiDepartment of mathematics,
Central Tehran Branch, Islamic
Azad University, Tehran, Iran.Hossein DoostieDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran.Journal Article20190603In this paper, we study the excess of continuous $K$-$g$-frames and give some results about this notion.<br />Also, we extend the concept of atomic system to continuous version and study its relations by continuous $K$-$g$-frames. Indeed, we give some equivalent characterizations for continuous $K$-$g$-frames. As well as, the relationship of a continuous $K$-$g$-frame and the range of operator $K$ will be verified. Finally, we study the induced $cK$-frames by continuous $K$-$g$-frames.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367120200801Amendment to the result on the trace of Haar wavelets matrixAmendment to the result on the trace of Haar wavelets matrix13224666810.22072/wala.2020.106628.1232ENA. Padmanabha ReddyDepartment of Studies in Mathematics, V. S. K. University, Ballari-583105, INDIA.Journal Article20190606 Trace and some other interesting properties of Haar wavelets matrix of size $2^K$ are studied by Shiralashetti and Kumbinarasaiah \cite{ref6}, results related to the trace of Haar wavelets matrix derived based on $K$ is even or odd and the same is concluded in Theorem $3.2$. This article deals with the trace of Haar wavelets matrix in depth by identifying and overcoming the pitfalls occur in the proof of Theorem 3.2.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367120200801ON CONTINUOUS WEAVING G-FRAMES IN HILBERT SPACESپیوستگی قابهای تعمیم یافته درهم تنیده در فضاهای هیلبرت23364667010.22072/wala.2020.114423.1248ENEsmaeil AlizadehDepartment of Mathematics, Marand Branch, Islamic Azad University, Marand, Islamic Republic of Iran.0000-0002-2786-6301Vahid SadriDepartment of Mathematics, Faculty of Tabriz Branch, Technical and Vocational University (TVU), East Azarbaijan, Islamic Republic of Iran.Journal Article20190918 In this note, we intend to introduce the concept of weaving continuous g-frames in Hilbert spaces. In addition, we present some new result for these frames and also we show that it is enough to check that on smaller measurable space than the given measurable space. We investigate the relationship between these frames and c-woven also, the sufficient and condition will be given. Finally, we verify the perturbation of weaving c-g-frames.در این مقاله ، ما قصد داریم مفهمومی از پیوستگی قاب های تعمیم یافته درهم تنیده در فضای هیلبرت را معرفی کنیم. آنگاه ، تعدادی نتایج جدیدی را روی این قابها ارائه می دهیم و همچنین نشان می دهیم برای قابهای تعمیم یافته درهم تنیده پیوسته کافی است آن را روی فضای اندازه پذیر کوچکتر از فضای اصلی بررسی کرد. ارتباط بین این قابها و قاب های پیوسته درهم تنیده بررسی می شود. همچنین شرایط کافی برای وجود این قابها ارائه می شود. بالاخره، پریشندگی قاب های تعمیم یافته درهم تنیده پیوسته مطالعه می کنیم.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367120200801Multiplication on double coset space $L^1(K\setminus G/H)$Multiplication on double coset space $L^1(K\setminus G/H)$37464668610.22072/wala.2020.119154.1262ENF. FahimianDepartment of Pure Mathematics, Ferdowsi University of Mashhad,
P.O.Box 1159-91775, Mashhad, Islamic Republic of Iran.R. A. Kamyabi-GolDepartment of Pure Mathematics, Ferdowsi University of Mashhad and Center of Excellence in Analysis on Algebric Structures (CEAAS) Islamic Republic of Iran.F. EsmaeelzadehDepartment of Mathematics, Bojnourd Branch, Islamic Azad university, Bojnourd, Islamic Republic of Iran.Journal Article20191225<br />Consider a locally compact group $G$ with two compact subgroups $H$ and $K$. Equip the double coset space $K\setminus G/H$ with the quotient topology. Suppose that $\mu$ is an $N$-relatively invariant measure, on $K\setminus G/H$. <br />We define a multiplication on $L^1(K\setminus G/H,\mu)$ such that this space becomes a Banach algebra that possesses a left (right) approximate identity.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367120200801Some properties of controlled K-frames in Hilbert spacesSome properties of controlled K-frames in Hilbert spaces47564668710.22072/wala.2020.119701.1266ENMohammad MahmoudiehDepartment of Mathematics, Damghan University, Damghan and Department of Basic Sciences, Faculty of Valiasr, Tehran Branch, Technical and Vocational University (TVU), Tehran, Islamic Republic of Iran.0000-0002-3240-5876Hessam HosseinnezhadDepartment of Basic Sciences, Faculty of Enghelab-e Eslami, Tehran Branch, Technical and Vocational University (TVU), Tehran, Islamic Republic of Iran.Gholamreza Abbaspour TabadkanDepartment of Mathematics, Damghan University, P.O.Box 36716-41167, Damghan, Islamic Republic of Iran.Journal Article20200106 In this paper, we reintroduce the concept of controlled K-frames and then, we show that this definition is equivalent<br />with the concept that has been recently introduced in \cite{Nouri}. Meanwhile, we correct<br />one of the results which was obtained in the mentioned paper. In the sequel, we construct some new controlled K-frames<br />by some operator theory tools. Finally, we provide some conditions under which the sum of two controlled K-frames remains<br />a controlled K-frame.Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-19367120200801Convex functions on compact $C^*$-convex setsتوابع محدب روی مجموعه های فشرده سی استار محدب57624668810.22072/wala.2020.120065.1268ENIsmail NikoufarDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Islamic Republic of Iran.0000-0002-7989-1613Journal Article20200113It is well known that if a real valued convex function on a compact convex domain<br />contained in the real numbers attains its maximum,<br />then it does so at least at one extreme point of its domain.<br />In this paper,<br />we consider a matrix convex function on a compact and $C^*$-convex set generated by self--adjoint matrices.<br />An important issue is so that this function on a compact and $C^*$-convex domain attains its maximum at a $C^*$-extreme point.