Continuity of CP-semigroups in the point-strong operator topology

Daniel Markiewicz, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We prove that if {φt}t≥0 is a CP-semigroup acting on a von Neu- mann algebra M ⊆B(H), then for every A ∈ M and ξ ∈ H, the map t CMSY10.-1.mapsto→ φt(A)ξ is norm-continuous. We discuss the implications of this fact to the existence of dilations of CP-semigroups to semigroups of endomorphisms.

Original languageEnglish
Pages (from-to)149-154
Number of pages6
JournalJournal of Operator Theory
Volume64
Issue number1
StatePublished - 1 Jun 2010
Externally publishedYes

Keywords

  • CP-semigroup, E-semigroup, Strong operator continuity, Bhat's dilation theorem, Dilations

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