The operator shift space

Timur Oikhberg

doi:10.1017/S0013091505000337

The operator shift space

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

Abstract

We construct and examine an operator space X, isometric to _2, such that every completely bounded map from its subspace Y into X is a compact perturbation of a linear combination of multiples of a shift of given multiplicity and their adjoints. Moreover, every completely bounded map on X is a Hilbert-Schmidt perturbation of such a linear combination.

Original language	English (US)
Pages (from-to)	229-263
Number of pages	35
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	51
Issue number	1
DOIs	https://doi.org/10.1017/S0013091505000337
State	Published - Feb 2008
Externally published	Yes

Keywords

Completely bounded maps
Completely indecomposable spaces
Operator spaces
Shift operator

ASJC Scopus subject areas

General Mathematics

Online availability

10.1017/S0013091505000337

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title = "The operator shift space",

abstract = "We construct and examine an operator space X, isometric to _2, such that every completely bounded map from its subspace Y into X is a compact perturbation of a linear combination of multiples of a shift of given multiplicity and their adjoints. Moreover, every completely bounded map on X is a Hilbert-Schmidt perturbation of such a linear combination.",

keywords = "Completely bounded maps, Completely indecomposable spaces, Operator spaces, Shift operator",

author = "Timur Oikhberg",

note = "Funding Information: Acknowledgements. The author was partly supported by NSF Grant no. DMS-0200714. He thanks the organizers of the workshop on Linear Analysis and Probability in College Station, TX, where part of this work was carried out. He is grateful to R. Douglas, B. Maurey and A. Zs{\'a}k for fruitful discussions on K-theory. Last but not least, he thanks the referee for useful advice on better organization of the paper and expanding its scope.",

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N1 - Funding Information: Acknowledgements. The author was partly supported by NSF Grant no. DMS-0200714. He thanks the organizers of the workshop on Linear Analysis and Probability in College Station, TX, where part of this work was carried out. He is grateful to R. Douglas, B. Maurey and A. Zsák for fruitful discussions on K-theory. Last but not least, he thanks the referee for useful advice on better organization of the paper and expanding its scope.

PY - 2008/2

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N2 - We construct and examine an operator space X, isometric to _2, such that every completely bounded map from its subspace Y into X is a compact perturbation of a linear combination of multiples of a shift of given multiplicity and their adjoints. Moreover, every completely bounded map on X is a Hilbert-Schmidt perturbation of such a linear combination.

AB - We construct and examine an operator space X, isometric to _2, such that every completely bounded map from its subspace Y into X is a compact perturbation of a linear combination of multiples of a shift of given multiplicity and their adjoints. Moreover, every completely bounded map on X is a Hilbert-Schmidt perturbation of such a linear combination.

KW - Completely bounded maps

KW - Completely indecomposable spaces

KW - Operator spaces

KW - Shift operator

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The operator shift space

Abstract

Keywords

ASJC Scopus subject areas

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