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Nuclear weighted conditional expectation operators

A. Ommi, Y. Estaremi

Abstract

We provide a characterisations of nuclear weighted conditional expectation operators between different $L^p(μ)$-spaces. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted conditional expectation operator between different $L^p(μ)$-spaces is the zero operator.

Nuclear weighted conditional expectation operators

Abstract

We provide a characterisations of nuclear weighted conditional expectation operators between different -spaces. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted conditional expectation operator between different -spaces is the zero operator.
Paper Structure (2 sections, 10 theorems, 53 equations)

This paper contains 2 sections, 10 theorems, 53 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Main Results

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 (19)

  • Definition 1.1
  • Definition 1.2: Weighted Conditional Expectation (WCE) Operator
  • Theorem 2.1: Pietsch domination theorem Diestel1995
  • Theorem 2.2
  • Theorem 2.3
  • Theorem 2.4
  • Corollary 2.5
  • proof
  • Corollary 2.6
  • proof
  • ...and 9 more