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Topologies on central extensions of von Neumann algebras

100%

Ayupov S., Kudaybergenov K., Djumamuratov R.

Open Mathematics

2012

tom 10

nr 2

656-664

Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra.

Automorphisms of central extensions of type I von Neumann algebras

100%

Albeverio S., Ayupov S., Kudaybergenov K., Djumamuratov R.

Studia Mathematica

2011

tom 207

nr 1

1-17

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.

Ograniczanie wyników

1 Open Mathematics

1 Studia Mathematica

2 Ayupov S.

2 Djumamuratov R.

2 Kudaybergenov K.

1 Albeverio S.

1 2012

1 2011

Wyniki wyszukiwania

Topologies on central extensions of von Neumann algebras

Automorphisms of central extensions of type I von Neumann algebras