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

Daniel Markiewicz; Orr Moshe Shalit

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

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7 Scopus citations

Abstract

We prove that if {φ_t}_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→ φ_t(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 language	English
Pages (from-to)	149-154
Number of pages	6
Journal	Journal of Operator Theory
Volume	64
Issue number	1
State	Published - 1 Jun 2010
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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AU - Shalit, Orr Moshe

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N2 - 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.

AB - 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.

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

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

Abstract

Keywords

ASJC Scopus subject areas

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