Schur Multipliers of Cartan Pairs

Publisher: Cambridge University Press

E-ISSN: 1464-3839|60|2|413-440

ISSN: 0013-0915

Source: Proceedings of the Edinburgh Mathematical Society, Vol.60, Iss.2, 2017-05, pp. : 413-440

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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 ( 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.