On an algebra of operators related to flnite traces on a von Neumann algebra

Given a von Neumann algebra M with a faithful normal flnite trace, we introduce the so called flnite tracial algebra Mf as the intersection of Lp-spaces Lp(M;„) over all p ‚ 1 and all faithful normal flnite traces „ on M: Basic algebraic and topological properties of these algebras are studied.

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