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arXiv · 1910.06891

Schur multipliers of Schatten--von Neumann classes $\boldsymbol{S_p}$

Aleksei Aleksandrov·Vladimir Peller
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Abstract

We study in this paper properties of Schur multipliers of Schatten von Neumann classes $\boldsymbol{S}_p$. We prove that for $p\le1$, Schur multipliers of $\boldsymbol{S}_p$ are necessarily completely bounded. We also introduce for $p\le1$ a scale ${\mathscr W}_p$ of tensor products of $\ell^\infty$ and prove that matrices in ${\mathscr W}_p$ are Schur multipliers of $\boldsymbol{S}_p$. We compare this sufficient condition with the sufficient condition of membership in the $p$-tensor product of $\ell^\infty$ spaces.

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BibTeXRIS

Aleksei Aleksandrov, Vladimir Peller. 2019-10-15. Schur multipliers of Schatten--von Neumann classes $\boldsymbol{S_p}$. https://arxiv.org/abs/1910.06891

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