On type II(0) E0-semigroups induced by q-pure maps on MnC
Abstract
Using a dilation theorem of Bhat, Powers has shown that every non-trivial spatial E0 -semigroup can be obtained from a CP -flow acting on B (K ⊗ L2 (0, ∞)), where K is a separable Hilbert space. In this thesis, we use boundary weight doubles ([straight phi], ν) to define natural boundary weight maps which then induce CP -flows over K for 1 < dim (K ) < ∞. Developing a comparison theory for the E 0 -semigroups arising from certain boundary weight doubles, we obtain examples of type II0HASH(0xb07eb5c0)E0 -semigroups and classify them up to cocycle conjugacy. We study the unital q -pure maps acting on Mn ([Special characters omitted.] ), classifying all such maps which are invertible or have rank one. We find that the rank one unital q -pure maps arise from faithful states on Mn ([Special characters omitted.] ) and, through a boundary weight construction using particular unbounded weights ν on B (L2 (0, ∞)), yield uncountably many mutually non-cocycle conjugate type II0HASH(0x198d48c8) E0 -semigroups for each 1 < n ∈ [Special characters omitted.] . We ask whether every unital q -pure map acting on Mn ([Special characters omitted.] ) has rank one or is invertible, and show that this is the case when n = 2. In conclusion, we discuss future problems involving the examination and generalization of these results.
Subject Area
Mathematics
Recommended Citation
Christopher Jankowski,
"On type II(0) E0-semigroups induced by q-pure maps on MnC"
(January 1, 2009).
Dissertations available from ProQuest.
Paper AAI3363373.
http://repository.upenn.edu/dissertations/AAI3363373
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