On a certain class of operator algebras and their derivations - Ayupov, Shavkat Abdullaevich; Abdullaev, Rustambay Zairovich; Kudaybergenov, Karimbergen Kadirbergenovich (Eurasian Mathematical Journal, 2014)
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 \( p ≥ 1 \) 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.