Multiplication Operators on Weighted Nakano (sss)

Author(s):

Awad A. Bakery ◽

Afaf R. Abou Elmatty ◽

OM Kalthum S. K. Mohamed

Keyword(s):

Sequence Space ◽

Sufficient Conditions ◽

Geometrical Structures

In this article, we investigate the sufficient conditions on weighted Nakano sequence space to be premodular Banach (sss). We examine some topological and geometrical structures of the multiplication operators defined on weighted Nakano prequasi-normed (sss).

Multiplication Operators on Orlicz Generalized Difference (sss)

Journal of Function Spaces ◽

10.1155/2020/6627966 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Awad A. Bakery ◽

OM Kalthum S. K. Mohamed

Keyword(s):

Sequence Space ◽

Sufficient Conditions ◽

Difference Sequence ◽

Geometrical Structures ◽

Difference Sequence Space

In this article, we inspect the sufficient conditions on the Orlicz generalized difference sequence space to be premodular Banach (sss). We look at some topological and geometrical structures of the multiplication operators described on Orlicz generalized difference prequasi normed (sss).

A note on Nakano generalized difference sequence space

Advances in Difference Equations ◽

10.1186/s13662-020-03082-1 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Awad A. Bakery ◽

Afaf R. Abou Elmatty

Keyword(s):

Sequence Space ◽

Sufficient Conditions ◽

Multiplication Operator ◽

Operator Ideal ◽

Difference Sequence ◽

Geometrical Structures ◽

Difference Sequence Space ◽

Special Space ◽

Type Sequence

Abstract In this paper, we investigate the necessary conditions on any s-type sequence space to form an operator ideal. As a result, we show that the s-type Nakano generalized difference sequence space X fails to generate an operator ideal. We investigate the sufficient conditions on X to be premodular Banach special space of sequences and the constructed prequasi-operator ideal becomes a small, simple, and closed Banach space and has eigenvalues identical with its s-numbers. Finally, we introduce necessary and sufficient conditions on X explaining some topological and geometrical structures of the multiplication operator defined on X.

On the domain of Riesz mean in the space Ls

Filomat ◽

10.2298/fil1704925y ◽

2017 ◽

Vol 31 (4) ◽

pp. 925-940 ◽

Cited By ~ 12

Author(s):

Medine Yeşilkayagil ◽

Feyzi Başar

Keyword(s):

Banach Space ◽

Sequence Space ◽

Double Sequence ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Double Sequences ◽

Riesz Mean ◽

Double Sequence Space ◽

Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

Mathematica Slovaca ◽

10.1515/ms-2021-0059 ◽

2021 ◽

Vol 71 (6) ◽

pp. 1375-1400

Author(s):

Feyzi Başar ◽

Hadi Roopaei

Keyword(s):

Lower Bound ◽

Sequence Space ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Matrix Transformations ◽

Infinite Matrix ◽

The Matrix ◽

Alpha Beta ◽

Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

Strongly omnipresent operators: general conditions and applications to composition operators

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700036764 ◽

2002 ◽

Vol 72 (3) ◽

pp. 335-348 ◽

Cited By ~ 6

Author(s):

L. Bernal-González ◽

M. C. Calderón-Moreno ◽

K.-G. Grosse-Erdmann

Keyword(s):

Linear Operator ◽

Composition Operators ◽

Sufficient Conditions ◽

Holomorphic Functions ◽

Complex Domain ◽

General Conditions

AbstractThis paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. An operator T on the space H(G) of holomorphic functions on a complex domain G is called strongly omnipresent whenever the set of T-monsters is residual in H(G), and a T-monster is a function f such that Tf exhibits an extremely ‘wild’ behaviour near the boundary. We obtain sufficient conditions under which an operator is strongly omnipresent, in particular, we show that every onto linear operator is strongly omnipresent. Using these criteria we completely characterize strongly omnipresent composition and multiplication operators.

On the Riesz Almost Convergent Sequences Space

Abstract and Applied Analysis ◽

10.1155/2012/691694 ◽

2012 ◽

Vol 2012 ◽

pp. 1-18 ◽

Cited By ~ 11

Author(s):

Mehmet Şengönül ◽

Kuddusi Kayaduman

Keyword(s):

Sequence Space ◽

Sufficient Conditions ◽

Riesz Transforms ◽

Necessary And Sufficient Conditions ◽

Infinite Matrices ◽

Convergent Sequences

The purpose of this paper is to introduce new spaces and that consist of all sequences whose Riesz transforms of order one are in the spaces and , respectively. We also show that and are linearly isomorphic to the spaces and , respectively. The and duals of the spaces and are computed. Furthermore, the classes and of infinite matrices are characterized for any given sequence space and determine the necessary and sufficient conditions on a matrix to satisfy , for all .

On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Abstract and Applied Analysis ◽

10.1155/2009/931020 ◽

2009 ◽

Vol 2009 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Karim Hedayatian ◽

Lotfollah Karimi

Keyword(s):

Hilbert Space ◽

Linear Operator ◽

Composition Operator ◽

Hardy Spaces ◽

Bounded Linear Operator ◽

Sufficient Conditions ◽

Weighted Hardy Spaces ◽

Bounded Linear ◽

Necessary And Sufficient

A bounded linear operatorTon a Hilbert spaceℋ, satisfying‖T2h‖2+‖h‖2≥2‖Th‖2for everyh∈ℋ, is called a convex operator. In this paper, we give necessary and sufficient conditions under which a convex composition operator on a large class of weighted Hardy spaces is an isometry. Also, we discuss convexity of multiplication operators.

On Some Properties of Cowen-Douglas Class of Operators

Journal of Function Spaces ◽

10.1155/2018/6078594 ◽

2018 ◽

Vol 2018 ◽

pp. 1-6 ◽

Author(s):

Parastoo Heiatian Naeini ◽

Bahmann Yousefi

Keyword(s):

Hilbert Space ◽

Analytic Function ◽

Essential Spectrum ◽

Analytic Functions ◽

Sufficient Conditions ◽

Multiplication Operator ◽

Space Of Analytic Functions ◽

Class Operator ◽

Necessary And Sufficient

We will consider multiplication operators on a Hilbert space of analytic functions on a domainΩ⊂C. For a bounded analytic functionφonΩ, we will give necessary and sufficient conditions under which the complement of the essential spectrum ofMφinφΩbecomes nonempty and this gives conditions for the adjoint of the multiplication operatorMφbelongs to the Cowen-Douglas class of operators. Also, we characterize the structure of the essential spectrum of a multiplication operator and we determine the commutants of certain multiplication operators. Finally, we investigate the reflexivity of a Cowen-Douglas class operator.

Multiplication operators on weighted spaces in the non-locally convex framework

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171297000112 ◽

1997 ◽

Vol 20 (1) ◽

pp. 75-79 ◽

Author(s):

L. A. Khan ◽

A. B. Thaheem

Keyword(s):

Topological Space ◽

Hausdorff Space ◽

Weighted Space ◽

Topological Algebra ◽

Sufficient Conditions ◽

Completely Regular ◽

General Topological Space ◽

Locally Convex

LetXbe a completely regular Hausdorff space,Ea topological vector space,Va Nachbin family of weights onX, andCV0(X,E)the weighted space of continuousE-valued functions onX. Letθ:X→Cbe a mapping,f∈CV0(X,E)and defineMθ(f)=θf(pointwise). In caseEis a topological algebra,ψ:X→Eis a mapping then defineMψ(f)=ψf(pointwise). The main purpose of this paper is to give necessary and sufficient conditions forMθandMψto be the multiplication operators onCV0(X,E)whereEis a general topological space (or a suitable topological algebra) which is not necessarily locally convex. These results generalize recent work of Singh and Manhas based on the assumption thatEis locally convex.

Operator Ideal of Cesaro Type Sequence Spaces Involving Lacunary Sequence

Abstract and Applied Analysis ◽

10.1155/2014/419560 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 2

Author(s):

Awad A. Bakery

Keyword(s):

Banach Spaces ◽

Sequence Space ◽

Sufficient Conditions ◽

Lacunary Sequence ◽

Operator Ideal ◽

Linear Operators ◽

Approximation Numbers ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Type Sequence

The aim of this paper is to give the sufficient conditions on the sequence spaceCesθ,pdefined in Lim (1977) such that the class of all bounded linear operators between any arbitrary Banach spaces withnth approximation numbers of the bounded linear operators inCesθ,pform an operator ideal.