Article

# On a certain class of operator algebras and their derivations

08/2009; DOI:abs/0908.1203
Source: arXiv

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 $p \geq 1$ 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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### Keywords

algebras

called finite tracial algebra $M_f$

faithful normal finite traces $\mu$

finite tracial algebras

topological properties

von Neumann algebra $M$