scholarly journals On the Essential Norm of Multiplications Operators Acting on Cesàro Sequence Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Julio C. Ramos-Fernández ◽  
María A. Rivera-Sarmiento ◽  
Margot Salas-Brown
Keyword(s):  
Dual Space ◽  
Measure Of Noncompactness ◽  
Multiplication Operator ◽  
Essential Norm ◽  
Sequence Spaces

In this article, we establish an important property about the growth of sequences in the dual space of Cesàro sequence spaces. As a consequence of this fact, we calculate the measure of noncompactness or the essential norm of the multiplication operator Mu acting on Cesàro sequence spaces cesp.

scholarly journals The essential norm of multiplication operators acting on Orlicz sequence spaces

2020 ◽  
Vol 39 (6) ◽  
pp. 1407-1414
Author(s):  
Julio C. Ramos-Fernández ◽  
Margot Salas-Brown
Keyword(s):  
Multiplication Operator ◽  
Essential Norm ◽  
Sequence Spaces ◽  
Multiplication Operators ◽  
Orlicz Sequence Spaces

We calculate the measure of non-compactness or the essential norm of the multiplication operator Mu acting on Orlicz sequence spaces lφ. As a consequence of our result, we obtain a known criteria for the compactness of multiplication operator acting on lφ.

scholarly journals Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Sei-Ichiro Ueki ◽  
Luo Luo
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Multiplication Operator ◽  
Essential Norm ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

We estimate the essential norm of a compact weighted composition operator acting between different Hardy spaces of the unit ball in . Also we will discuss a compact multiplication operator between Hardy spaces.

scholarly journals On some spaces of summable sequences and their duals

1986 ◽  
Vol 9 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Geraldo Soares de Souza ◽  
G. O. Golightly
Keyword(s):  
Bounded Variation ◽  
Dual Space ◽  
Sequence Spaces ◽  
Simple Argument

Suppose thatSis the space of all summable sequencesαwith‖α‖S=supn≥0|∑j=n∞αj|andJthe space of all sequencesβof bounded variation with‖β‖J=|β0|+∑j=1∞|βj−βj−1|. Then forαinSandβinJ |∑j=0∞αjβj|≤‖α‖S‖β‖J; this inequality leads to the description of the dual space ofSasJ. It, related inequalities, and their consequences are the content of this paper. In particular, the inequality cited above leads directly to the Stolz form of Abel's theorem and provides a very simple argument. Also, some other sequence spaces are discussed.

On difference sequence spaces of fractional-order involving Padovan numbers

2020 ◽  
pp. 2150095
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
Syed Abdul Mohiuddine
Keyword(s):  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Difference Operator ◽  
Sequence Spaces ◽  
Difference Sequence ◽  
Topological Properties ◽  
Hausdorff Measure Of Noncompactness ◽  
Order Difference ◽  
Matrix Formula ◽  
Difference Sequence Spaces

In this paper, we introduce Padovan difference sequence spaces of fractional-order [Formula: see text] [Formula: see text] [Formula: see text] by the composition of the fractional-order difference operator [Formula: see text] and the Padovan matrix [Formula: see text] defined by [Formula: see text] and [Formula: see text] respectively, where the sequence [Formula: see text] is the Padovan sequence. We give some topological properties, Schauder basis and [Formula: see text]-, [Formula: see text]- and [Formula: see text]-duals of the newly defined spaces. We characterize certain matrix classes related to the [Formula: see text] space. Finally, we characterize certain classes of compact operators on [Formula: see text] using Hausdorff measure of noncompactness.

Application of Measure of Noncompactness to Infinite Systems of Differential Equations

2013 ◽  
Vol 56 (2) ◽  
pp. 388-394 ◽  
Author(s):  
M. Mursaleen
Keyword(s):  
Differential Equations ◽  
Sequence Space ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Sequence Spaces ◽  
Measures Of Noncompactness ◽  
Infinite Systems ◽  
Systems Of Differential Equations ◽  
Banach Sequence Spaces ◽  
Banach Sequence

AbstractIn this paper we determine theHausdorff measure of noncompactness on the sequence space n(ϕ) ofW. L. C. Sargent. Further we apply the technique of measures of noncompactness to the theory of infinite systems of differential equations in the Banach sequence spaces n(ϕ) and m(ϕ). Our aim is to present some existence results for infinite systems of differential equations formulated with the help of measures of noncompactness.

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