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arXiv · 1604.00198

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

Julio Delgado·Michael Ruzhansky·Baoxiang Wang
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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 $\mathbb R^n$ and functions of the harmonic oscillator in terms of the global symbol.

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Julio Delgado, Michael Ruzhansky, Baoxiang Wang. 2016-04-01. Grothendieck-Lidskii trace formula for mixed-norm and variable Lebesgue spaces. https://arxiv.org/abs/1604.00198

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