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Classification of E_0-Semigroups by Product Systems

Michael Skeide (Autor)

Buch | Softcover

126 Seiten

2016
American Mathematical Society (Verlag)
978-1-4704-1738-3 (ISBN)

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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.

Michael Skeide, Universita degli Studi del Molise, Campobaso, Italy.

Introduction
Morita equivalence and representations
Stable Morita equivalence for Hilbert modules
Ternary isomorphisms
Cocycle conjugacy of $E_0$-semigroups $E_0$-semigroups, product systems, and unitary cocycles
Conjugate $E_0$-semigroups and Morita equivalent product systems
Stable unitary cocycle (inner) conjugacy of $E_0$-semigroups
About continuity
Hudson-Parthasarathy dilations of spatial Markov semigroups
Von Neumann case: Algebraic classification
Von Neumann case: Topological classification
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
References

Erscheinungsdatum	02.04.2016
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	207 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-1738-3 / 1470417383
ISBN-13	978-1-4704-1738-3 / 9781470417383
Zustand	Neuware