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 , where is an inner automorphism implemented by an element a ∈ E(M), and is a special automorphism generated by an automorphism ϕ of the center of E(M). In particular if M is of type then every band preserving automorphism of E(M) is inner.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-1,
author = {Sergio Albeverio and Shavkat Ayupov and Karimbergen Kudaybergenov and Rauaj Djumamuratov},
title = {Automorphisms of central extensions of type I von Neumann algebras},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {1-17},
zbl = {1246.46058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-1}
}
Sergio Albeverio; Shavkat Ayupov; Karimbergen Kudaybergenov; Rauaj Djumamuratov. Automorphisms of central extensions of type I von Neumann algebras. Studia Mathematica, Tome 204 (2011) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-1/