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Schur Multipliers of Cartan Pairs

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  13 June 2016

R. H. Levene ,
N. Spronk ,
I. G. Todorov  and
L. Turowska
R. H. Levene
Affiliation:
School of Mathematics & Statistics, University College Dublin, Belfield, Dublin 4, Ireland ([email protected])
N. Spronk
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada ([email protected])
I. G. Todorov
Affiliation:
Pure Mathematics Research Centre, Queen's University Belfast, Belfast BT7 1NN, UK ([email protected])
L. Turowska
Affiliation:
Department of Mathematics, Chalmers University of Technology and the University of Gothenburg, 412 96 Göteborg, Sweden ([email protected])
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Abstract

We define the Schur multipliers of a separable von Neumann algebra with Cartan maximal abelian self-adjoint algebra , generalizing the classical Schur multipliers of (ℓ2). We characterize these as the normal -bimodule maps on . If contains a direct summand isomorphic to the hyperfinite II1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product ⊗eh are strictly contained in the algebra of all Schur multipliers.

Keywords

Schur multiplierCartan MASAbimodule map

MSC classification

Secondary: 46L10: General theory of von Neumann algebras 46L07: Operator spaces and completely bounded maps
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 2 , May 2017 , pp. 413 - 440
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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