Tensor Products of Noncommutative Lp-Spaces

Somlak Utudee

doi:10.5402/2012/197468

Abstract

We consider the notion of tensor product of noncommutative Lp spaces associated with finite von Neumann algebras and define the notion of tensor product of Haagerup noncommutative Lp spaces associated with σ-finite von Neumann algebras.

Highlights

Introduction and PreliminariesThe main goal of this paper is explanation of the notion of tensor products of noncommutative Lp-spaces associated with von Neumann algebras
Let M be a von Neumann algebra equipped with a faithful normal semifinite trace τ
Let M be a von Neumann algebra on a Hilbert space H, Aut M the group of all ∗automorphism of M, G a locally compact group equipped with its left Haar measure dg and

Summary

Introduction and Preliminaries

The main goal of this paper is explanation of the notion of tensor products of noncommutative Lp-spaces associated with von Neumann algebras. The notion of tensor products of noncommutative probability spaces was considered by Xu in 1. We will generalized that notations to the cases of noncommutative Lp-spaces associated with von Neumann algebras. We give some necessary preliminaries on noncommutative Lpspaces associated with von Neumann algebras and tensor product of von Neumann algebras

Noncommutative Lp-Spaces Associated with Semifinite von Neumann Algebras

Tensor Products of von Neumann Algebras