Classification of E_0-Semigroups by Product Systems

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

• IntroductionMorita equivalence and representationsStable Morita equivalence for Hilbert modulesTernary isomorphismsCocycle conjugacy of $E_0$-semigroups $E_0$-semigroups, product systems, and unitary cocyclesConjugate $E_0$-semigroups and Morita equivalent product systemsStable unitary cocycle (inner) conjugacy of $E_0$-semigroupsAbout continuityHudson-Parthasarathy dilations of spatial Markov semigroupsVon Neumann case: Algebraic classificationVon Neumann case: Topological classificationVon Neumann case: Spatial Markov semigroupsAppendix A: Strong type I product systemsAppendix B: $E_0$-semigroups and representations for strongly continuous product systemsReferences