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A CONJUGACY CRITERION FOR PURE E0-SEMIGROUPS
 

Summary: A CONJUGACY CRITERION FOR PURE
E0-SEMIGROUPS
REMUS FLORICEL
Abstract. We show that the conjugacy class of an arbitrary pure
E0-semigroup is completely determined by its class of normal cocy-
cles. If the E0-semigroup admits a normal invariant state, then its
conjugacy class is determined by the class of cocycles that stabilize
density lists.
Introduction
Introduced by R.T. Powers in [7], E0-semigroups are -weak contin-
uous one-parameter semigroups = {t}t0 of unital *-endomorphisms
of the von Neumann algebra B(H) of all bounded linear operators on a
separable Hilbert space H (see ref. [3] for a comprehensive treatment
of the subject).
Two central results of the theory of E0-semigroups assert that (i)
every spatial E0-semigroup is cocycle conjugate to an E0-semigroup in
standard form [8], and; (ii) the conjugacy classes of the E0-semigroups
in standard form within the cocycle conjugacy class of a spatial E0-
semigroup correspond to the orbits of the action of the local unitary
-cocycles on the set of semigroups of intertwining isometries of [1].

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics