Schur multipliers of Cartan pairs

We define the Schur multipliers of a separable von Neumann algebra M with Cartan maximal abelian self-adjoint algebra A, generalizing the classical Schur multipliers of B(2). We characterize 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⊗ehA are strictly contained in the algebra of all Schur multipliers