Automorphisms of central extensions of type I von Neumann algebras

Abstract

Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of $M.$ 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 $T=T_a\circ T_{\varphi },$ where $T_a(x)=ax{a}^{-1}$ is an inner automorphism implemented by an element $a\in E(M),$ and $T_{\varphi }$ is a special automorphism generated by an automorphism $\varphi$ 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.

16 pages

References in corpus (1)

• Additive derivations on algebras of measurable operators