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 GrothendieckLidskii 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 arXiv:
 arXiv:1503.07202
 Bibcode:
 2015arXiv150307202D
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Spectral Theory;
 46B28;
 47B10 (Primary);
 47G10;
 47B06 (Secondary)
 EPrint:
 18 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