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A note on local automorphisms

Ajda Fošner (2006)

Czechoslovak Mathematical Journal

Let H be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of ( H ) , the algebra of all bounded linear operators on a Hilbert space H , is an automorphism.

Automorphisms of central extensions of type I von Neumann algebras

Sergio Albeverio, Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov (2011)

Studia Mathematica

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 ) = a x a - 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...

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