W*-corresponcences, Finite Directed Graphs and Markov Chains: W*-algebras, Graph Algebras and Markov Chains - Victor Vega - Bøger - VDM Verlag Dr. Müller - 9783639155242 - 26. maj 2009
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W*-corresponcences, Finite Directed Graphs and Markov Chains: W*-algebras, Graph Algebras and Markov Chains

Victor Vega

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元 423,75

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W*-corresponcences, Finite Directed Graphs and Markov Chains: W*-algebras, Graph Algebras and Markov Chains

Let A be the W*-algebra, L1(E(0),µ), where E(0) is a fnite set and µ is a probability measure with full support. Let P: A->A be a completely positive unital map. In the present context, P is given by a stochastic matrix. We study the properties of P that are refected in the dilation theory developed by Muhly and Solel in Int. J. Math. 13, 2002. Let H be the Hilbert space L2(E(0),µ) and let pi : A -> B(H) the representation of A given by multiplication. Form the Stinespring space H1. Then X is a W*-correspondence over P is expressed through a completely contractive representation T of X on H. This representation can be dilated to an isometric representation V of X on a Hilbert space that contains H. We show that X is naturally isomorphic to the correspondence associated to the directed graph E whose vertex space is E(0) and whose edge space is the support of the matrix representing P - a subset of E(0)×E(0). Further, V is shown to be essentially a Cuntz-Krieger representation of E. We also study the simplicity and the ideal structure of the graph C*-algebra associated to the stochastic matrix P.

Medie Bøger     Paperback Bog   (Bog med blødt omslag og limet ryg)
Udgivet 26. maj 2009
ISBN13 9783639155242
Forlag VDM Verlag Dr. Müller
Antal sider 120
Mål 197 g
Sprog Tysk