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arXiv · 0908.1203

On a certain class of operator algebras and their derivations

Sh. A. Ayupov·R. Z. Abdullaev·K. K. Kudaybergenov
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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 $L_p(M, μ)$ over all $p \geq 1$ and over all faithful normal finite traces $μ$ 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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Sh. A. Ayupov, R. Z. Abdullaev, K. K. Kudaybergenov. 2009-08-09. On a certain class of operator algebras and their derivations. https://arxiv.org/abs/0908.1203

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