GLOBAL STRUCTURE IN THE SEMIGROUP OF ENDOMORPHISMS ON A VON NEUMANN ALGEBRA

摘要

In [17], we studied the natural u-topology on the endomorphism semigroup End(JW) of a von Neumann algebra M, given by pointwise conver-gence in the prediial. For many purposes, however, the topological approach seems to be difficult. In this paper, the Borel structure induced by the u-topology on Bnd{A/) is then investigated- hi particular a Borel implementa-tion of endomorphisms is found and applied to prove that invariants snch as the dimension mapping are Rorel. 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 Rnd(M) are discussed.