Abstract

We introduce a noncommutative version of Schur multipliers relative to an operator ideal. In this setting the functions of two variables are replaced by elements from a tensor product of C*-algebras, and the measures (or spectral measures) by representations. For commutative C*-algebras this approach agrees with Birman and Solomyak’s theory of double operator integrals. We study the dependence of the spaces of multipliers on the choice of representations and find that the question is closely related to Voiculescu and Arveson’s theory of approximately equivalent representations. The space of multipliers universal with respect to the chosen measures is related to the Haagerup tensor product of the algebras.

Keywords

C*-algebra, representation, approximate equivalence, tensor product, Schur multiplier, operator ideal, ω-continuity

Mathematical Subject Classification

Primary: 46L06, 47B49

Secondary: 47B10, 47L20

Authors