 

Robert T. Powers
Continuous spatial semigroups of completely positive maps of B(H)


Published: 
November 19, 2003

Keywords: 
completely positive maps, *endomorphisms, E_{o}semigroups 
Subject: 
Primary 46L57; Secondary 46L55 


Abstract
This paper concerns the structure of strongly continuous one parameter
semigroups of completely positive contractions of B(H)
= B(K ⊗ L^{2}(0,∞)) which are intertwined by
translation. These are called CPflows over K . Using Bhat's
dilation result each unital CPflow over K dilates to an
E_{o}semigroup of B(H_{1}) where H_{1} can be
considered to contain B(K ⊗ L^{2}(0,∞)). Every
spatial E_{o}semigroup is cocycle conjugate to one dilated from a
CPflow. Each CPflow is determined by its associated boundary weight
map which determines the generalized boundary representation. The index of
the E_{o}semigroup dilated from a CPflow is calculated. Machinery for
determining whether two CPflow dilate to cocycle conjugate
E_{o}semigroups is developed.


Author information
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104
rpowers@math.upenn.edu
http://www.math.upenn.edu/~rpowers/

