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 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 norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

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.

Essential norm estimates of weighted composition operators between Bergman spaces on strongly pseudoconvex domains

2007 ◽  
Vol 142 (3) ◽  
pp. 525-533 ◽  
Author(s):  
ŽELJKO ČUČKOVIĆ ◽  
RUHAN ZHAO
Keyword(s):  
Composition Operators ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Pseudoconvex Domains ◽  
Weighted Composition Operators ◽  
Norm Estimates ◽  
Strongly Pseudoconvex Domains ◽  
Weighted Composition

AbstractWe give estimates of the essential norms of weighted composition operators acting between Bergman spaces on strongly pseudoconvex domains. We also characterize boundedness and compactness of these 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 Essential norm estimates for Hankel operators on convex domains in $\mathbb{C}^2$

2017 ◽  
Vol 120 (2) ◽  
pp. 305
Author(s):  
Željko Čučković ◽  
Sönmez Şahutoğlu
Keyword(s):  
Convex Domain ◽  
Hankel Operator ◽  
Smooth Boundary ◽  
Essential Norm ◽  
Hankel Operators ◽  
Convex Domains ◽  
Norm Estimates ◽  
Bounded Convex Domain ◽  
Derivatives Of ◽  
Bounded Convex

Let $\Omega \subset \mathbb{C}^2$ be a bounded convex domain with $C^1$-smooth boundary and $\varphi \in C^1(\overline{\Omega})$ such that $\varphi $ is harmonic on the non-trivial disks in the boundary. We estimate the essential norm of the Hankel operator $H_{\varphi }$ in terms of the $\overline{\partial}$ derivatives of $\varphi$ “along” the non-trivial disks in the boundary.

scholarly journals Inequalities Involving Essential Norm Estimates of Product-Type Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Manisha Devi ◽  
Ajay K. Sharma ◽  
Kuldip Raj
Keyword(s):  
Analytic Function ◽  
Holomorphic Function ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Open Unit ◽  
Open Unit Disk ◽  
Norm Estimates ◽  
Type Spaces ◽  
Weighted Composition ◽  
Dirichlet Type Spaces

Consider an open unit disk D = z ∈ ℂ : z < 1 in the complex plane ℂ , ξ a holomorphic function on D , and ψ a holomorphic self-map of D . For an analytic function f , the weighted composition operator is denoted and defined as follows: W ξ , ψ f z = ξ z f ψ z . We estimate the essential norm of this operator from Dirichlet-type spaces to Bers-type spaces and Bloch-type spaces.

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
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