Completely bounded Schur multipliers of Schatten-von Neumann class $S_p, 0 < p < 1$.

5 Jul 2021, 15:00


Vladimir Peller (Michigan State University)


I am going to speak about my joint results with A.B. Aleksandrov. Gilles Pisier posed the problem of whether a matrix Schur multiplier of the Schatten—von Neumann class $S_p$ for $1 < p < \infty$, $p\neq 2$, has to be completely bounded. We have proved that this is true in the case $0< p < 1$. We also consider various sufficient conditions for an infinite matrix to be a Schur multiplier of $S_p$. In particular, we introduce a $p$-analog of the Haagerup tensor product of $\ell^\infty$ spaces.

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Vladimir Peller (Michigan State University)

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