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arXiv · 0911.4304

Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

Cédric Arhancet
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Abstract

We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra $A_p(G)$ on the natural predual of the operator space $\frak{M}_{p,cb}$ of completely bounded Schur multipliers on Schatten space $S_p$. We determine the isometric Schur multipliers and prove that the space $\frak{M}_{p}$ of bounded Schur multipliers on Schatten space $S_p$ is the closure in the weak operator topology of the span of isometric multipliers.

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Cédric Arhancet. 2009-11-23. Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers. https://doi.org/10.1007/s00020-011-1872-5

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