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# The involutive automorphisms of $\tau$-compact operators affiliated with a type I von Neuman algebra

### Abstract

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.

### Article Information

 Title The involutive automorphisms of $\tau$-compact operators affiliated with a type I von Neuman algebra Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 1, 54-59 MathSciNet MR2402152 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

K. K. Kudaybergenov
Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Khodjaev, Tashkent, 100125, Uzbekistan

T. S. Kalandarov
Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 29 F. Khodjaev, Tashkent, 100125, Uzbekistan

### Citation Example

K. K. Kudaybergenov and T. S. Kalandarov, The involutive automorphisms of $\tau$-compact operators affiliated with a type I von Neuman algebra, Methods Funct. Anal. Topology 14 (2008), no. 1, 54-59.

### BibTex

@article {MFAT440,
AUTHOR = {Kudaybergenov, K. K. and Kalandarov, T. S.},
TITLE = {The involutive automorphisms of $\tau$-compact operators  affiliated with a type I von Neuman algebra},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {1},
PAGES = {54-59},
ISSN = {1029-3531},
MRNUMBER = {MR2402152},
URL = {http://mfat.imath.kiev.ua/article/?id=440},
}