Automorphisms of central extensions of type I von Neumann algebras

Mathematics – Operator Algebras

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

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.

Rate now

     

Profile ID: LFWR-SCP-O-544714

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.