E0-dilation of strongly commuting CP0-semigroups

Orr Moshe Shalit

doi:10.1016/j.jfa.2008.04.003

E₀-dilation of strongly commuting CP₀-semigroups

Orr Moshe Shalit

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We prove that every strongly commuting pair of CP₀-semigroups has a minimal E₀-dilation. This is achieved in two major steps, interesting in themselves: (1) we show that a strongly commuting pair of CP₀-semigroups can be represented via a two parameter product system representation; (2) we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation. In particular, we obtain that every commuting pair of CP₀-semigroups on B (H), H finite-dimensional, has an E₀-dilation.

Original language	English
Pages (from-to)	46-89
Number of pages	44
Journal	Journal of Functional Analysis
Volume	255
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2008.04.003
State	Published - 1 Jul 2008
Externally published	Yes

Keywords

CP-semigroups
Completely contractive covariant representation
Dilation
E-semigroups
Product system
Representation
Strong commutativity
Two-parameter semigroups

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2008.04.003

Cite this

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title = "E0-dilation of strongly commuting CP0-semigroups",

abstract = "We prove that every strongly commuting pair of CP0-semigroups has a minimal E0-dilation. This is achieved in two major steps, interesting in themselves: (1) we show that a strongly commuting pair of CP0-semigroups can be represented via a two parameter product system representation; (2) we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation. In particular, we obtain that every commuting pair of CP0-semigroups on B (H), H finite-dimensional, has an E0-dilation.",

keywords = "CP-semigroups, Completely contractive covariant representation, Dilation, E-semigroups, Product system, Representation, Strong commutativity, Two-parameter semigroups",

author = "Shalit, {Orr Moshe}",

note = "Funding Information: 1 The author is supported by the Jacobs School of Graduate Studies and the Department of Mathematics at the Technion—I.I.T, and by the Gutwirth Fellowship. This research is part of the author{\textquoteright}s PhD thesis, done under the supervision of Professor Baruch Solel. Fax: +972 4 8293388.",

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AU - Shalit, Orr Moshe

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N2 - We prove that every strongly commuting pair of CP0-semigroups has a minimal E0-dilation. This is achieved in two major steps, interesting in themselves: (1) we show that a strongly commuting pair of CP0-semigroups can be represented via a two parameter product system representation; (2) we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation. In particular, we obtain that every commuting pair of CP0-semigroups on B (H), H finite-dimensional, has an E0-dilation.

AB - We prove that every strongly commuting pair of CP0-semigroups has a minimal E0-dilation. This is achieved in two major steps, interesting in themselves: (1) we show that a strongly commuting pair of CP0-semigroups can be represented via a two parameter product system representation; (2) we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation. In particular, we obtain that every commuting pair of CP0-semigroups on B (H), H finite-dimensional, has an E0-dilation.

KW - CP-semigroups

KW - Completely contractive covariant representation

KW - Dilation

KW - E-semigroups

KW - Product system

KW - Representation

KW - Strong commutativity

KW - Two-parameter semigroups

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