Automorphisms of central extensions of type I von Neumann algebras

• Autorzy: Sergio Albeverio , Shavkat Ayupov , Karimbergen Kudaybergenov , Rauaj Djumamuratov
• Języki publikacji: EN

Abstrakty

EN

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 $T = T_{a} ∘ T_{ϕ}$, where $T_{a}(x) = axa^{-1}$ is an inner automorphism implemented by an element a ∈ E(M), and $T_{ϕ}$ is a special automorphism generated by an automorphism ϕ of the center of E(M). In particular if M is of type $I_{∞}$ then every band preserving automorphism of E(M) is inner.

Kategorie tematyczne

• 46L52: Noncommutative function spaces
• 46L40: Automorphisms
• 46L51: Noncommutative measure and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 207
• Numer: 1
• Strony: 1-17

Daty

wydano

2011

Twórcy

autor

Sergio Albeverio

• Institut für Angewandte Mathematik and HCM, Rheinische Friedrich-Wilhelms-Universität Bonn, 53115 Bonn, Germany

autor

Shavkat Ayupov

• Institute of Mathematics and Information Technologies, Uzbekistan Academy of Sciences, 100125 Tashkent, Uzbekistan
• Abdus Salam International Centre, for Theoretical Physics (ICTP), Trieste, Italy

autor

Karimbergen Kudaybergenov

• Karakalpak State University, 230113 Nukus, Uzbekistan

autor

Rauaj Djumamuratov

• Karakalpak State University, 230113 Nukus, Uzbekistan

Identyfikatory

DOI

10.4064/sm207-1-1