Compactness properties of operator multipliers

K. Juschenko, R. H. Levene*, I. G. Todorov, L. Turowska

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We continue the study of multidimensional operator multipliers initiated in [K. Juschenko, I.G. Todorov, L. Turowska, Multidimensional operator multipliers, Trans. Amer. Math. Soc., in press]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar [H. Saar, Kompakte, vollständig beschränkte Abbildungen mit Werten in einer nuklearen C*-Algebra, Diplomarbeit, Universität des Saarlandes, Saarbrücken, 1982].

Original languageEnglish (US)
Pages (from-to)3772-3805
Number of pages34
JournalJournal of Functional Analysis
Volume256
Issue number11
DOIs
StatePublished - Jun 1 2009

Keywords

  • Complete compactness
  • Haagerup tensor product
  • Operator multiplier
  • Schur multiplier

ASJC Scopus subject areas

  • Analysis

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    Juschenko, K., Levene, R. H., Todorov, I. G., & Turowska, L. (2009). Compactness properties of operator multipliers. Journal of Functional Analysis, 256(11), 3772-3805. https://doi.org/10.1016/j.jfa.2008.12.018