Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

Details Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

2009-11-23

arxiv.org/abs/0911.4304v6

Integral Equations and Operator Theory, Volume 70, Number 4, 485-510 (2011)

Mathematics

Operator Algebras

24 pages; corrected typos

Scientific paper

10.1007/s00020-011-1872-5

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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