Multiplication and composition operators between two Orlicz spaces

Yousef Estaremi

arXiv:1301.4830·math.FA·October 22, 2013·33 cites

Multiplication and composition operators between two Orlicz spaces

Yousef Estaremi

PDF

Open Access

TL;DR

This paper studies the properties of multiplication and composition operators between two Orlicz spaces, focusing on their boundedness, compactness, and essential norm based on the transformation, function, and measure space.

Contribution

It provides new characterizations of boundedness, compactness, and essential norm for these operators in the context of Orlicz spaces, which are less explored in existing literature.

Findings

01

Characterization of boundedness conditions

02

Criteria for compactness of operators

03

Formulas for essential norm in terms of measure space properties

Abstract

In this paper we consider composition operator $C_{φ} g e n er a t e d b y n o n s in g u l a r m e a s u r ab l e t r an s f or ma t i o n$ T $an d m u l t i pl i c a t i o n o p er a t or$ M_u $g e n er a t e d b y m e a s u r ab l e f u n c t i o n$ u $b e tw ee n tw o d i f f er e n tO r l i cz s p a ces, t h e n w e in v es t i g a t e b o u n d e d n ess, co m p a c t n ess an d esse n t ia l n or m o f m u l t i pl i c a t i o nan d co m p os i t i o n o p er a t or s in t er m o f p r o p er t i eso f t h e ma pp in g$ \varphi $, t h e f u n c t i o n$ u $an d t h e m e a s u r es p a ce$ (X, \Sigma, \mu)$.

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.

Taxonomy

TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Approximation Theory and Sequence Spaces