K. K. Kudaybergenov
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The involutive automorphisms of $\tau$-compact operators affiliated with a type I von Neuman algebra
MFAT 14 (2008), no. 1, 54-59
Let $M$ be a type I von Neumann algebra with a center $Z,$ and a faithful normal semi-finite trace $\tau.$ Consider the algebra $L(M, \tau)$ of all $\tau$-measurable operators with respect to $M$ and let $S_0(M, \tau)$ be the subalgebra of $\tau$-compact operators in $L(M, \tau).$ We prove that any $Z$-linear involutive automorphisms of $S_0(M, \tau)$ is inner.
MFAT 12 (2006), no. 3, 234-242
The paper is devoted to studying $\nabla$-Fredholm operators in Banach--Kantorovich spaces over a ring of measurable functions. We show that a bounded linear operator acting in Banach--Kantorovich space is $\nabla$-Fredholm if and only if it can be represented as a sum of an invertible operator and a cyclically compact operator.