Classification of E_0-Semigroups by Product Systems

ISBN-13: 9781470417383 / Angielski

Michael Skeide

Opis

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.

Spis treści

• 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