# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Automorphisms of central extensions of type I von Neumann algebras

### Tom 207 / 2011

Studia Mathematica 207 (2011), 1-17 MSC: Primary 46L40; Secondary 46L51, 46L52. DOI: 10.4064/sm207-1-1

#### Streszczenie

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.

#### Autorzy

• Sergio AlbeverioInstitut für Angewandte Mathematik and HCM
Rheinische Friedrich-Wilhelms-Universität Bonn
53115 Bonn, Germany
e-mail
• Shavkat AyupovInstitute of Mathematics and Information Technologies
Uzbekistan Academy of Sciences
100125 Tashkent, Uzbekistan
and
Abdus Salam International Centre
for Theoretical Physics (ICTP)
Trieste, Italy
e-mail
• Karimbergen KudaybergenovKarakalpak State University
230113 Nukus, Uzbekistan
e-mail
• Rauaj DjumamuratovKarakalpak State University
230113 Nukus, Uzbekistan
e-mail

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