Sahand Communications in Mathematical Analysis
Volume:8 Issue: 1, Autumn 2017

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.

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.

Let (X,d) be an infinite compact metric space, let (B,∥.∥) be a unital Banach space, and take α∈(0,1). In this work, at first we define the big and little α -Lipschitz vector-valued (B-valued) operator algebras, and consider the little α -lipschitz B -valued operator algebra, lip α (X,B) . Then we characterize its second dual space.

Let X be an infinite set, equipped with a topology τ . In this paper we studied the relationship between τ , 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.

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of β∗ -closed sets in topological space to present and study a new class of functions called contra β∗ -continuous and almost contra β∗ -continuous functions as a new generalization of contra continuity.

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.

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.

A sequence {T n } ∞ n=1 of bounded linear operators on a separable infinite dimensional Hilbert space H is called subspace-diskcyclic with respect to the closed subspace M⊆H, if there exists a vector x∈H such that the disk-scaled orbit {αT n x:n∈N,α∈C,|α|≤1}∩M {αTnx:n∈N,α∈C,|α|≤1}∩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 . 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 to be subspace-diskcyclic(subspace-hypercyclic).