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Grothendieck-Lidskii trace formula for mixed-norm and variable Lebesgue spaces (1604.00198v1)

Published 1 Apr 2016 in math.FA, math.OA, and math.SP

Abstract: In this note we present the metric approximation property for weighted mixed-norm $L_w{(p_1,\dots ,p_n)}$ 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 $\mathbb Rn$ and functions of the harmonic oscillator in terms of the global symbol.

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