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

Julio Delgado | Zendy; Michael Ruzhansky | Zendy; Baoxiang Wang | Zendy

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

Author(s) -

Julio Delgado,

Michael Ruzhansky,

Baoxiang Wang

Publication year - 2016

Publication title -

journal of spectral theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.063

H-Index - 19

eISSN - 1664-0403

pISSN - 1664-039X

DOI - 10.4171/jst/141

Subject(s) - lp space , mathematics , pure mathematics , norm (philosophy) , trace (psycholinguistics) , lebesgue integration , banach space , philosophy , epistemology , linguistics

In this note we present the metric approximation property for weighted mixed-norm L (p1,...,pn) w 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 R n and functions of the harmonic oscillator in terms of global symbols

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