Grothendieck–Lidskii trace formula for mixed-norm and variable Lebesgue spaces

  • Julio Delgado

    Imperial College London, UK
  • Michael Ruzhansky

    Imperial College London, UK
  • Baoxiang Wang

    Peking University, Beijing, China

Abstract

In this note we present the metric approximation property for weighted mixed-norm and variable exponent Lebesgue type spaces. As a consequence, this also implies the same property for modulation and Wiener-Amalgam spaces. We then characterise nuclear operators on such spaces and state the corresponding Grothendieck–Lidskii trace formulae. We apply the obtained results to derive criteria for nuclearity and trace formulae for periodic operators on Rn and functions of the harmonic oscillator in terms of global symbols.

Cite this article

Julio Delgado, Michael Ruzhansky, Baoxiang Wang, Grothendieck–Lidskii trace formula for mixed-norm and variable Lebesgue spaces. J. Spectr. Theory 6 (2016), no. 4, pp. 781–791

DOI 10.4171/JST/141