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Classification of $E_0$-Semigroups by Product Systems
| eBook ISBN: | 978-1-4704-2826-6 |
| Product Code: | MEMO/240/1137.E |
| List Price: | $84.00 |
| MAA Member Price: | $75.60 |
| AMS Member Price: | $50.40 |
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Classification of $E_0$-Semigroups by Product Systems
| eBook ISBN: | 978-1-4704-2826-6 |
| Product Code: | MEMO/240/1137.E |
| List Price: | $84.00 |
| MAA Member Price: | $75.60 |
| AMS Member Price: | $50.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 240; 2015; 126 pp
In these notes the author presents a complete theory of classification of \(E_0\)-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
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Table of Contents
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Chapters
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1. Introduction
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2. Morita equivalence and representations
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3. Stable Morita equivalence for Hilbert modules
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4. Ternary isomorphisms
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5. Cocycle conjugacy of $E_0$–semigroups
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6. $E_0$–Semigroups, product systems, and unitary cocycles
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7. Conjugate $E_0$–Semigroups and Morita equivalent product systems
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8. Stable unitary cocycle (inner) conjugacy of $E_0$–semigroups
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9. About continuity
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10. Hudson-Parthasarathy dilations of spatial Markov semigroups
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11. Von Neumann case: Algebraic classification
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12. Von Neumann case: Topological classification
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13. Von Neumann case: Spatial Markov semigroups
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Appendix A: Strong type I product systems
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Appendix B: $E_0$–Semigroups and representations for strongly continuous product systems
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Volume: 240; 2015; 126 pp
In these notes the author presents a complete theory of classification of \(E_0\)-semigroups by product systems of correspondences. As an application of his theory, he answers the fundamental question if a Markov semigroup admits a dilation by a cocycle perturbations of noise: It does if and only if it is spatial.
-
Chapters
-
1. Introduction
-
2. Morita equivalence and representations
-
3. Stable Morita equivalence for Hilbert modules
-
4. Ternary isomorphisms
-
5. Cocycle conjugacy of $E_0$–semigroups
-
6. $E_0$–Semigroups, product systems, and unitary cocycles
-
7. Conjugate $E_0$–Semigroups and Morita equivalent product systems
-
8. Stable unitary cocycle (inner) conjugacy of $E_0$–semigroups
-
9. About continuity
-
10. Hudson-Parthasarathy dilations of spatial Markov semigroups
-
11. Von Neumann case: Algebraic classification
-
12. Von Neumann case: Topological classification
-
13. Von Neumann case: Spatial Markov semigroups
-
Appendix A: Strong type I product systems
-
Appendix B: $E_0$–Semigroups and representations for strongly continuous product systems
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.