Affiliation:
1. Department of Mathematics , IISER Bhopal , Bhopal , MP 462066 , India
Abstract
Abstract
A classical result by Effros
connects the barycentric decomposition of a state on a C*-algebra to the disintegration theory of the GNS representation of the state with respect to an orthogonal measure on the state space of the C*-algebra. In this note, we take this approach to the space of unital completely positive maps on a C*-algebra with values in
B
(
H
)
{B(H)}
, connecting the barycentric decomposition of the unital completely positive map and the disintegration theory of the minimal Stinespring dilation of the same. This generalizes Effros’ work in the non-commutative setting. We do this by introducing a special class of barycentric measures which we call generalized orthogonal measures. We end this note by mentioning some examples of generalized orthogonal measures.
Subject
Applied Mathematics,General Mathematics
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