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Vietnam Journal of Mathematics 34:3(2006) 353-356

 The Embedding of Haagerup L^p Spaces

Phan Viet Thu

Abstract.  The aim of this paper is to give a proof for a theorem due to S. Goldstein that: If there is a σ-weakly continuous faithful projection of norm one from a von Neumann algebra $M$ onto its von Neumann subalgebra N, then L^p(N) can be canonically embeded into L^p(M). Here L^p(A) [6] (M. Terp. L^p-spaces Associated with von Neumann Algebras, Notes Kξ benhavns Universitet, Matematisk Institut, No. 3, 1981) denotes the Haagerup L^p space over the von Neumann algebra A.

2000 Mathematics Subject Classification: 46L52, 81R15.

Keywords: von Newmann algebras, haagerup spaces, conditional expection for von Neumann algebras.

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