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Nuclear Weighted composition operators between different $L^p$-spaces

S. Al Ghafri, Y. Estaremi, S. Shamsigamchi

Abstract

We provide complete characterisations of nuclear weighted composition operators between two distinct $L^p(μ)$-spaces, where $1\leq p<\infty$. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted composition operator between $L^p(μ)$-spaces is the zero operator.

Nuclear Weighted composition operators between different $L^p$-spaces

Abstract

We provide complete characterisations of nuclear weighted composition operators between two distinct -spaces, where . As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted composition operator between -spaces is the zero operator.
Paper Structure (2 sections, 10 theorems, 32 equations)

This paper contains 2 sections, 10 theorems, 32 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Nuclear weighted composition operators

Key Result

Theorem 2.1

Let $1\le p<\infty$ and let $T:X\to Y$ be absolutely $p$--summing. Then there exist $C>0$ and a Borel probability measure $\mu$ on the weak$^{*}$--compact unit ball $B_{X^*}$ such that In particular, for $p=1$,

Theorems & Definitions (14)

  • Theorem 2.1: Pietsch domination theorem dj
  • Theorem 2.2
  • proof
  • Corollary 2.3
  • Corollary 2.4
  • Theorem 2.5
  • proof
  • Corollary 2.6
  • Corollary 2.7
  • Theorem 2.8
  • ...and 4 more