On a certain class of operator algebras and their derivations

Details On a certain class of operator algebras and their derivations On a certain class of operator algebras and their derivations

2009-08-09

arxiv.org/abs/0908.1203v1

Mathematics

Operator Algebras

Scientific paper

Given a von Neumann algebra $M$ with a faithful normal finite trace, we introduce the so called finite tracial algebra $M_f$ as the intersection of $L_p$-spaces $L_p(M, \mu)$ over all $p \geq 1$ and over all faithful normal finite traces $\mu$ on $M.$ Basic algebraic and topological properties of finite tracial algebras are studied. We prove that all derivations on these algebras are inner.

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