Non-isomorphism of 𝐿_{𝑝}-spaces associated with finite and infinite von Neumann algebras

Sukochev, F.

doi:10.1090/S0002-9939-96-03279-0

Non-isomorphism of $L_p$-spaces associated with finite and infinite von Neumann algebras
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Proc. Amer. Math. Soc. 124 (1996), 1517-1527 Request permission

Abstract:

If $(M_{1},\tau _{1})$ is a finite von Neumann algebra and if $(M_{2},\tau _{2})$ is an infinite (semifinite) von Neumann algebra, then $L_{p}(M_{1},\tau _{1})$ and $L_{p}(M_{2},\tau _{2})$ are non-isomorphic for all $p\in (1,\infty ), p\neq 2$ .

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