Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

Abstract

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

24 pages; corrected typos

References in corpus (5)

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• Cycles and 1-unconditional matrices
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Cited by in corpus (2)

• A characterization of completely bounded normal Jordan $\ast$-homomorphisms on von Neumann algebras
• Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers I