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Schur Multipliers of Cartan Pairs

Published online by Cambridge University Press:  13 June 2016

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])

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 (2). 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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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