We extend the de Branges-Beurling theorem characterizing shift-invariant spaces boundedly contained in Hardy space of square-summable power series to full Fock over Cd. Here, is identified as Non-commutative (NC) Space Taylor several non-commuting variables. then proceed study lattice operations on NC kernels and operator-valued multipliers between vector-valued spaces. In particular, we demons...

We give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions (polyFock spaces), displaying a ”Nyquist rate” which increases with the degree of polyanaliticity. This is done introducing a unitary mapping between vector valued Hilbert spaces and poly-Fock spaces. This mapping extends Bargmann ́s theory to polyanalytic spaces. T...

We study a new system of nonlinear set-valued variational inclusions involving a finite family of H ·, · -accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of H ·, · -accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme...

in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-con...

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces L X , where X is a Banach space and 1 ≤ p < ∞, and extend the result to vector-valued Banach function spaces EX , where E is a Banach function space with order continuous norm. Let X be a Banach space. The problem of describing the compact sets in the Lebesgue-Bochner spaces LpX , ...

In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space E, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of R, and we discuss their extension to E. We introduce the notion of E-metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of con...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...

Let X be an arbitrary nonempty set and a lattice of subsets of X such that ∅, X ∈ . Let ( ) denote the algebra generated by and I( ) denote those nontrivial, zero-one valued, finitely additive measures on ( ). In this paper, we discuss some of the normal characterizations of lattices in terms of the associated lattice regular measures, filters and outer measures. We consider the interplay betwe...