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Classification of $E_0$-Semigroups by Product Systems

Michael Skeide Università degli Studi del Molise, Campobaso, Italy
Available Formats:
Electronic ISBN: 978-1-4704-2826-6
Product Code: MEMO/240/1137.E
List Price: $84.00 MAA Member Price:$75.60
AMS Member Price: $50.40 Click above image for expanded view Classification of$E_0$-Semigroups by Product Systems Michael Skeide Università degli Studi del Molise, Campobaso, Italy Available Formats:  Electronic 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
• Book Details

Memoirs of the American Mathematical Society
Volume: 2402015; 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
• 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
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Volume: 2402015; 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
• Appendix B: $E_0$–Semigroups and representations for strongly continuous product systems