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 language | English (US) |
---|---|
Pages (from-to) | 3772-3805 |
Number of pages | 34 |
Journal | Journal of Functional Analysis |
Volume | 256 |
Issue number | 11 |
DOIs | |
State | Published - Jun 1 2009 |
Funding
The first named author was supported by The Royal Swedish Academy of Sciences, Knut och Alice Wallenbergs Stiftelse and Jubileumsfonden of the University of Gothenburg’s Research Foundation. The second and the third named authors were supported by Engineering and Physical Sciences Research Council grant EP/D050677/1. The last named author was supported by the Swedish Research Council.
Keywords
- Complete compactness
- Haagerup tensor product
- Operator multiplier
- Schur multiplier
ASJC Scopus subject areas
- Analysis