A Class of C*-Algebras and Topological Markov Chains.
Let be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of , the algebra of all bounded linear operators on a Hilbert space , is an automorphism.
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...