Schur multipliers of Cartan pairs

Abstract

We define the Schur multipliers of a separable von Neumann algebra M with Cartan masa A, generalising the classical Schur multipliers of $B({\ell }^2)$. We characterise these as the normal A-bimodule maps on M. If M contains a direct summand isomorphic to the hyperfinite II_1 factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product $A{\otimes }_{eh}A$ are strictly contained in the algebra of all Schur multipliers.

References in corpus (2)

• On the ranges of bimodule projections
• Bimodules over Cartan MASAs in von Neumann Algebras, Norming Algebras, and Mercer's Theorem