Abstract
It is known that every semigroup of normal completely positive maps
P=
P
t
:t≥0
of
B(H)
, satisfying
P
t
(1)=1
for every
t≥0
, has a minimal dilation to an E_0-semigroup acting on
B(K)
for some Hilbert space K containing H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the index of P agrees with the index of its minimal dilation to an E_0-semigroup. However, no examples were discussed, and no computations were made. In this paper we calculate the index of a unital completely positive semigroup whose generator is a bounded operator
L:B(H)→B(H)
in terms of natrual structures associated with the generator. This includes all unital CP semigroups acting on matrix algebras. We also show that the minimal dilation of the semigroup
P=exptL:t≥0
to an \esg\ is is cocycle conjugate to a CAR/CCR flow.