Ordered involutive operator spaces

David P. Blecher; Kay Kirkpatrick; Matthew Neal; Wend Werner

doi:10.1007/s11117-007-2086-6

Ordered involutive operator spaces

David P. Blecher, Kay Kirkpatrick, Matthew Neal, Wend Werner

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

Abstract

This is a companion to recent papers of the authors; here we construct the 'noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the boundary preserve order. As an application, we consider 'maximal' and 'minimal' unitizations of such ordered operator spaces.

Original language	English (US)
Pages (from-to)	497-510
Number of pages	14
Journal	Positivity
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/s11117-007-2086-6
State	Published - Aug 2007
Externally published	Yes

Keywords

C*- envelope
Loewner order
Noncommutative Shilov boundary
Operator spaces
Operator system
Positive operator
Unitization

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
General Mathematics

Online availability

10.1007/s11117-007-2086-6

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title = "Ordered involutive operator spaces",

abstract = "This is a companion to recent papers of the authors; here we construct the 'noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the boundary preserve order. As an application, we consider 'maximal' and 'minimal' unitizations of such ordered operator spaces.",

keywords = "C*- envelope, Loewner order, Noncommutative Shilov boundary, Operator spaces, Operator system, Positive operator, Unitization",

author = "Blecher, {David P.} and Kay Kirkpatrick and Matthew Neal and Wend Werner",

note = "Funding Information: Blecher was partially supported by grant DMS 0400731 from the National Science Foundation. Kirkpatrick was partially supported by an NSF REU grant. Neal was supported by Denison University. Werner was supported by the SFB 487 Geometrische Strukturen in der Mathematik, at the Westf{\"a}lische Wilhelms-Universit{\"a}t, supported by the Deutsche Forschungsgemeinschaft.",

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AU - Blecher, David P.

AU - Kirkpatrick, Kay

AU - Neal, Matthew

AU - Werner, Wend

N1 - Funding Information: Blecher was partially supported by grant DMS 0400731 from the National Science Foundation. Kirkpatrick was partially supported by an NSF REU grant. Neal was supported by Denison University. Werner was supported by the SFB 487 Geometrische Strukturen in der Mathematik, at the Westfälische Wilhelms-Universität, supported by the Deutsche Forschungsgemeinschaft.

PY - 2007/8

Y1 - 2007/8

N2 - This is a companion to recent papers of the authors; here we construct the 'noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the boundary preserve order. As an application, we consider 'maximal' and 'minimal' unitizations of such ordered operator spaces.

AB - This is a companion to recent papers of the authors; here we construct the 'noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the boundary preserve order. As an application, we consider 'maximal' and 'minimal' unitizations of such ordered operator spaces.

KW - C- envelope

KW - Loewner order

KW - Noncommutative Shilov boundary

KW - Operator spaces

KW - Operator system

KW - Positive operator

KW - Unitization

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JO - Positivity

JF - Positivity

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ER -

Ordered involutive operator spaces

Abstract

Keywords

ASJC Scopus subject areas

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