Schur Multipliers of Cartan Pairs

Abstract

AbstractWe define the Schur multipliers of a separable von Neumann algebrawith Cartan maximal abelian self-adjoint algebra, generalizing the classical Schur multipliers of(ℓ2). We characterize these as the normal-bimodule maps on. Ifcontains a direct summand isomorphic to the hyperfinite II1factor, then we show that the Schur multipliers arising from the extended Haagerup tensor product⊗ehare strictly contained in the algebra of all Schur multipliers.