On a certain class of operator algebras and their derivations

Abstract

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 $p\ge 1$ 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.

References in corpus (1)

• Derivations in algebras of operator-valued functions