The bounded approximation property of variable Lebesgue spaces and nuclearity

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.

arXiv comment18 pages. The paper has been updated by adding a remark (on page 6) on a link between bounded and metric approximation properties. This should be the final version to appear in Math Scand