The Essential Norm of Multiplication Operators on Lorentz Sequence Spaces

2016 ◽  
Vol 41 (1) ◽  
pp. 245 ◽  
Author(s):  
René E. Castillo ◽  
Julio C. Ramos-Fernández ◽  
Margot Salas-Brown
Keyword(s):  
Essential Norm ◽  
Sequence Spaces ◽  
Multiplication Operators

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 Multiplication Operators on Cesàro Sequence Spaces

2016 ◽  
Vol 49 (4) ◽  
Author(s):  
B. S. Komal ◽  
Suruchi Pandoh ◽  
Kuldip Raj
Keyword(s):  
Sequence Spaces ◽  
Multiplication Operators

AbstractIn this paper we characterize the compact, invertible and Fredholm multiplication operators on Cesàro sequence spaces.

EQUIVALENCE OF SEMI-NORMS RELATED TO SUPER WEAKLY COMPACT OPERATORS

2021 ◽  
pp. 1-13
Author(s):  
KUN TU
Keyword(s):  
Banach Spaces ◽  
Quantitative Method ◽  
Approximation Property ◽  
Essential Norm ◽  
Compact Operators ◽  
Sequence Spaces ◽  
Weakly Compact ◽  
The Family ◽  
Compact Approximation ◽  
Weakly Compact Operators

Abstract We study super weakly compact operators through a quantitative method. We introduce a semi-norm $\sigma (T)$ of an operator $T:X\to Y$ , where X, Y are Banach spaces, the so-called measure of super weak noncompactness, which measures how far T is from the family of super weakly compact operators. We study the equivalence of the measure $\sigma (T)$ and the super weak essential norm of T. We prove that Y has the super weakly compact approximation property if and and only if these two semi-norms are equivalent. As an application, we construct an example to show that the measures of T and its dual $T^*$ are not always equivalent. In addition we give some sequence spaces as examples of Banach spaces having the super weakly compact approximation property.

Multiplication operators on Orlicz-Lorentz sequence spaces

2013 ◽  
Vol 7 ◽  
pp. 1461-1469 ◽  
Author(s):  
Pawan Bala ◽  
Anuradha Gupta ◽  
Neha Bhatia
Keyword(s):  
Sequence Spaces ◽  
Multiplication Operators

scholarly journals Multiplication Operators between Lipschitz-Type Spaces on a Tree

2011 ◽  
Vol 2011 ◽  
pp. 1-36 ◽  
Author(s):  
Robert F. Allen ◽  
Flavia Colonna ◽  
Glenn R. Easley
Keyword(s):  
Essential Norm ◽  
Operator Norm ◽  
Multiplication Operators ◽  
Norm Estimates ◽  
Infinite Tree ◽  
Type Spaces ◽  
Bounded Functions ◽  
The Difference ◽  
Complex Valued

Let be the space of complex-valued functions on the set of vertices of an infinite tree rooted at such that the difference of the values of at neighboring vertices remains bounded throughout the tree, and let be the set of functions such that , where is the distance between and and is the neighbor of closest to . In this paper, we characterize the bounded and the compact multiplication operators between and and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between and the space of bounded functions on and determine their operator norm and their essential norm. We establish that there are no isometries among the multiplication operators between these spaces.

Essential norm estimates for multiplication operators on $$L_p(\mu )$$ spaces

2021 ◽  
Author(s):  
René E. Castillo ◽  
Yesid A. Lemus-Abril ◽  
Julio C. Ramos-Fernández
Keyword(s):  
Essential Norm ◽  
Multiplication Operators ◽  
Norm Estimates

scholarly journals Multiplication Operators on Cesàro-Orlicz Sequence Spaces

2016 ◽  
Vol 57 (1) ◽  
pp. 137-145 ◽  
Author(s):  
Kuldip Raj ◽  
Charu Sharma ◽  
Suruchi Pandoh
Keyword(s):  
Sequence Spaces ◽  
Multiplication Operators ◽  
Closed Range ◽  
Orlicz Sequence Spaces

AbstractIn this paper, we characterize the compact, invertible, Fredholm and closed range multiplication operators on Cesàro-Orlicz sequence spaces.

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.

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