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Robert T. Powers
Continuous spatial semigroups of completely positive maps of B(H)
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Published: |
November 19, 2003
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Keywords: |
completely positive maps, *-endomorphisms, Eo-semigroups |
Subject: |
Primary 46L57; Secondary 46L55 |
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Abstract
This paper concerns the structure of strongly continuous one parameter
semigroups of completely positive contractions of B(H)
= B(K ⊗ L2(0,∞)) which are intertwined by
translation. These are called CP-flows over K . Using Bhat's
dilation result each unital CP-flow over K dilates to an
Eo-semigroup of B(H1) where H1 can be
considered to contain B(K ⊗ L2(0,∞)). Every
spatial Eo-semigroup is cocycle conjugate to one dilated from a
CP-flow. Each CP-flow is determined by its associated boundary weight
map which determines the generalized boundary representation. The index of
the Eo-semigroup dilated from a CP-flow is calculated. Machinery for
determining whether two CP-flow dilate to cocycle conjugate
Eo-semigroups is developed.
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Author information
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104
rpowers@math.upenn.edu
http://www.math.upenn.edu/~rpowers/
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