The bounded approximation property of variable Lebesgue spaces and nuclearity

TL;DR

This paper establishes the bounded approximation property and nuclearity of variable Lebesgue spaces, and applies these results to trace formulas and criteria for periodic operators on Euclidean spaces.

Contribution

It introduces the nuclearity concept for variable Lebesgue spaces and connects it with trace formulas, extending the theory to periodic operators.

Findings

Proves the bounded approximation property for variable Lebesgue spaces.

Studies nuclearity and derives criteria for nuclearity in these spaces.

Applies results to trace formulas for periodic operators on a0a0^n.

Abstract

In this paper we prove the bounded approximation property for variable exponent Lebesgue spaces, study the concept of nuclearity on such spaces and apply it to trace formulae such as the Grothendieck-Lidskii formula. We apply the obtained results to derive criteria for nuclearity and trace formulae for periodic operators on $\mathbb R^n$ in terms of global symbols.