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

@article{Delgado2016GrothendieckLidskiiTF,
  title={Grothendieck-Lidskii trace formula for mixed-norm and variable Lebesgue spaces},
  author={J. Delgado and Michael Ruzhansky and Baoxiang Wang},
  journal={arXiv: Functional Analysis},
  year={2016}
}
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… 
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