Journal of Operator Theory

Volume 37, Issue 2, Spring 1997 pp. 341-356.

Global structure in the semigroup of endomorphisms on a von Neumann algebra

Authors: Carl Winsløw
Author institution:Matematisk Institut, Københavns Universitet, 2100 København Ø, DENMARK

Summary: In [17], we studied the natural u-topology on the endomorphism semigroup End(M) of a von Neumann algebra M, given by pointwise convergence in the predual. For many purposes, however, the topological approach seems to be difficult. In this paper, the Borel structure induced by the u-topology on End(M) is then investigated. In particular a Borel implementation of endomorphisms is found and applied to prove that invariants such as the dimension mapping are Borel. Moreover we prove that End(M) is Borel isomorphic to the cartesian product of automorphisms and subfactors of M, and some related problems for quotient spaces of End(M) are discussed.

Keywords: Endomorphisms, von Neumann algebras, Borel structure.

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