$G$-Frames for operators in Hilbert spaces
Bahram
Dastourian
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.
author
Mohammad
Janfada
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, P.O. Box 1159-91775, Iran.
author
text
article
2017
eng
$K$-frames as a generalization of frames were introduced by L. G\u{a}vru\c{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new generalization of $K$-frames. After proving some characterizations of generalized $K$-frames, new results are investigated and some new perturbation results are established. Finally, we give several characterizations of $K$-duals.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
1
21
https://scma.maragheh.ac.ir/article_23646_5b6f187d7a7e622a7634cf56284bc2c6.pdf
dx.doi.org/10.22130/scma.2017.23646
Generalized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series
Sanjib Kumar
Datta
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN- 741235, West Bengal, India.
author
Tanmay
Biswas
Rajbari, Rabindrapalli, R. N. Tagore Road,
P.O.-Krishnagar, Dist-Nadia, PIN-741101, West Bengal, India.
author
Jinarul Haque
Shaikh
Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal, India.
author
text
article
2017
eng
In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
23
32
https://scma.maragheh.ac.ir/article_22636_d44441b3c78ee5e56778a0617e77ab53.pdf
dx.doi.org/10.22130/scma.2017.22636
Second dual space of little $\alpha$-Lipschitz vector-valued operator algebras
Abbasali
Shokri
Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran.
author
text
article
2017
eng
Let $(X,d)$ be an infinite compact metric space, let $(B,\parallel . \parallel)$ be a unital Banach space, and take $\alpha \in (0,1).$ In this work, at first we define the big and little $\alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $\alpha$-lipschitz $B$-valued operator algebra, $lip_{\alpha}(X,B)$. Then we characterize its second dual space.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
33
41
https://scma.maragheh.ac.ir/article_23072_37fba52745f4bc2b7c6107415e1dffc2.pdf
dx.doi.org/10.22130/scma.2017.23072
Generated topology on infinite sets by ultrafilters
Alireza
Bagheri Salec
Department of Mathematics, Faculty of Science, University of Qom, P.O.Box 3716146611, Qom, Iran.
author
text
article
2017
eng
Let $X$ be an infinite set, equipped with a topology $\tau$. In this paper we studied the relationship between $\tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
43
53
https://scma.maragheh.ac.ir/article_23337_6c78346b95a2ee9f22a0f2d5078a421e.pdf
dx.doi.org/10.22130/scma.2017.23337
Contra $\beta^{*}$-continuous and almost contra $\beta^{*}$-continuous functions
Appachi
Vadivel
Department of Mathematics, Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.
author
Radhakrishnan
Ramesh
Department of Mathematics, Pope John Paul II College of Education, Reddiar Palayam, Puducherry-605010, India.
author
Duraisamy
Sivakumar
Department of Mathematics (DDE), Annamalai University, Annamalai Nagar-608 002, Tamil Nadu, India.
author
text
article
2017
eng
The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of $\beta^{*}$-closed sets in topological space to present and study a new class of functions called contra $\beta^{*}$-continuous and almost contra $\beta^{*}$-continuous functions as a new generalization of contra continuity.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
55
71
https://scma.maragheh.ac.ir/article_22045_9b9885af1b47833c61470ac4706d0a25.pdf
dx.doi.org/10.22130/scma.2017.22045
Stability of additive functional equation on discrete quantum semigroups
Maysam
Maysami Sadr
Department of Mathematics, Institute for Advanced Studies in Basic Sciences, P.O.Box 45195-1159, Zanjan 45137-66731, Iran.
author
text
article
2017
eng
We construct a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result generalizes a famous and old result due to Forti on the Hyers-Ulam stability of additive functional equations on amenable classical discrete semigroups.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
73
81
https://scma.maragheh.ac.ir/article_22852_a21e351c5081462f3ee9b1f99cdd027a.pdf
dx.doi.org/10.22130/scma.2017.22852
Compare and contrast between duals of fusion and discrete frames
Elnaz
Osgooei
Department of Sciences, Urmia University of Technology, P.O.Box 419-57155, Urmia, Iran.
author
Ali akbar
Arefijammal
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box 397, Sabzevar, Iran.
author
text
article
2017
eng
Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion frames with their associated discrete frames.
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
83
96
https://scma.maragheh.ac.ir/article_22412_6e582d16caaf2352781eab207dfc817c.pdf
dx.doi.org/10.22130/scma.2017.22412
Subspace-diskcyclic sequences of linear operators
Mohammad Reza
Azimi
Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh, Iran.
author
text
article
2017
eng
A sequence $\{T_n\}_{n=1}^{\infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space $\mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $M\subseteq \mathcal{H},$ if there exists a vector $x\in \mathcal{H}$ such that the disk-scaled orbit $\{\alpha T_n x: n\in \mathbb{N}, \alpha \in\mathbb{C}, | \alpha | \leq 1\}\cap M$ is dense in $M$. The goal of this paper is the studying of subspace diskcyclic sequence of operators like as the well known results in a single operator case. In the first section of this paper, we study some conditions that imply the diskcyclicity of $\{T_n\}_{n=1}^{\infty}$. In the second section, we survey some conditions and subspace-diskcyclicity criterion (analogue the results obtained by some authors in \cite{MR1111569, MR2261697, MR2720700}) which are sufficient for the sequence $\{T_n\}_{n=1}^{\infty}$ to be subspace-diskcyclic(subspace-hypercyclic).
Sahand Communications in Mathematical Analysis
University of Maragheh
2322-5807
08
v.
1
no.
2017
97
106
https://scma.maragheh.ac.ir/article_23850_39a0664f6ddf12b1b192462ffddd7aaf.pdf
dx.doi.org/10.22130/scma.2017.23850