- We will send in 10–14 business days.
/images/books/13176814/9783639155242.jpg)
- Author: Victor Vega
- Publisher: VDM Verlag
- ISBN-10: 3639155246
- ISBN-13: 9783639155242
- Format: 15.2 x 22.9 x 0.7 cm, minkšti viršeliai
- Language: English
- SAVE -10% with code: EXTRA
W*-Corresponcences, Finite Directed Graphs and Markov Chains (e-book) (used book) | bookbook.eu
Reviews
Description
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)ÃE(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.
EXTRA 10 % discount with code: EXTRA
The promotion ends in 23d.19:14:14
The discount code is valid when purchasing from 10 €. Discounts do not stack.
- Author: Victor Vega
- Publisher: VDM Verlag
- ISBN-10: 3639155246
- ISBN-13: 9783639155242
- Format: 15.2 x 22.9 x 0.7 cm, minkšti viršeliai
- Language: English English
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)ÃE(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.
Reviews