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Journal of Operator Theory

Volume 68, Issue 2, Fall 2012  pp. 335-363.

$E_0$-semigroups: around and beyond Arveson's work

Authors:  Masaki Izumi
Author institution: Department of Mathematics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502 Japan

Summary:  We give an account of the theory of $E_0$-semigroups. We first focus on Arveson's contributions to the field and related results. Then we present the recent development of type II and type III $E_0$-semigroups. We also include a short note in Appendix, based on Arveson's observation, on noncommutative Poisson boundaries.

Keywords:  $E_0$-semigroups, product systems, $CP$-semigroups, dilation

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