Abstract
In this work, we introduce a noncommutative analogue of the Figà-Talamanca–Herz algebra A p (G) on the natural predual of the operator space \({\frak{M}_{p,cb}}\) of completely bounded Schur multipliers on the Schatten space S p . We determine the isometric Schur multipliers and prove that the space \({\frak{M}_{p}}\) of bounded Schur multipliers on the Schatten space S p is the closure in the weak operator topology of the span of isometric multipliers.
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This work is partially supported by ANR 06-BLAN-0015.
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Arhancet, C. Noncommutative Figà-Talamanca–Herz Algebras for Schur Multipliers. Integr. Equ. Oper. Theory 70, 485–510 (2011). https://doi.org/10.1007/s00020-011-1872-5
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DOI: https://doi.org/10.1007/s00020-011-1872-5