Automorphisms of central extensions of type I von Neumann algebras
Volume 207 / 2011
Studia Mathematica 207 (2011), 1-17
MSC: Primary 46L40; Secondary 46L51, 46L52.
DOI: 10.4064/sm207-1-1
Abstract
Given a von Neumann algebra $M$ we consider its central extension $E(M)$. For type I von Neumann algebras, $E(M)$ coincides with the algebra $LS(M)$ of all locally measurable operators affiliated with $M.$ In this case we show that an arbitrary automorphism $T$ of $E(M)$ can be decomposed as $T=T_a\circ T_\phi ,$ where $T_a(x)=axa^{-1}$ is an inner automorphism implemented by an element $a\in E(M),$ and $T_\phi $ is a special automorphism generated by an automorphism $\phi $ of the center of $E(M).$ In particular if $M$ is of type I$_\infty $ then every band preserving automorphism of $E(M)$ is inner.
