 
Summary: A CONJUGACY CRITERION FOR PURE
E0SEMIGROUPS
REMUS FLORICEL
Abstract. We show that the conjugacy class of an arbitrary pure
E0semigroup is completely determined by its class of normal cocy
cles. If the E0semigroup 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], E0semigroups are weak contin
uous oneparameter 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 E0semigroups assert that (i)
every spatial E0semigroup is cocycle conjugate to an E0semigroup in
standard form [8], and; (ii) the conjugacy classes of the E0semigroups
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].
