Mathematics – Operator Algebras
Scientific paper
2011-04-25
Mathematics
Operator Algebras
16 pages
Scientific paper
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 $T=T_a\circ T_\phi,$ 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.
Albeverio Sergio
Ayupov Sh. A.
Djumamuratov R. T.
Kudaybergenov Karimbergen K.
No associations
LandOfFree
Automorphisms of central extensions of type I von Neumann algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Automorphisms of central extensions of type I von Neumann algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Automorphisms of central extensions of type I von Neumann algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-544714