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Vietnam Journal of Mathematics 34:3(2006) 353-356  The Embedding of Haagerup $L^p$ Spaces Pham 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 $\sigma$-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 K$\psi$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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