On the central Haagerup tensor product and completely bounded mappings of a C*-algebra

Robert J Archbold; Douglas W B Somerset; R. M. Timoney

doi:10.1016/j.jfa.2005.03.006

On the central Haagerup tensor product and completely bounded mappings of a C*-algebra

Robert J Archbold, Douglas W B Somerset, R. M. Timoney

Mathematical Science

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

13 Citations (Scopus)

Abstract

We consider the natural contractive map from the central Haagerup, tensor product of a unital C*-algebra A with itself to the space of completely bounded maps CB(A) on A. We establish the necessity of the known sufficient condition for isometry of the map, namely that all Glimm ideals of A are primal. However, when the map is restricted to tensors with length bounded by a fixed quantity, a weaker necessary and sufficient condition is established. (c) 2005 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	406-428
Number of pages	22
Journal	Journal of Functional Analysis
Volume	226
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2005.03.006
Publication status	Published - Sept 2005

Keywords

Glimm ideal
primal ideal
matrix numerical range
PRIMAL IDEALS
STAR-ALGEBRAS
MAPS

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10.1016/j.jfa.2005.03.006

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title = "On the central Haagerup tensor product and completely bounded mappings of a C*-algebra",

abstract = "We consider the natural contractive map from the central Haagerup, tensor product of a unital C*-algebra A with itself to the space of completely bounded maps CB(A) on A. We establish the necessity of the known sufficient condition for isometry of the map, namely that all Glimm ideals of A are primal. However, when the map is restricted to tensors with length bounded by a fixed quantity, a weaker necessary and sufficient condition is established. (c) 2005 Elsevier Inc. All rights reserved.",

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T1 - On the central Haagerup tensor product and completely bounded mappings of a C*-algebra

AU - Archbold, Robert J

AU - Somerset, Douglas W B

AU - Timoney, R. M.

PY - 2005/9

Y1 - 2005/9

N2 - We consider the natural contractive map from the central Haagerup, tensor product of a unital C*-algebra A with itself to the space of completely bounded maps CB(A) on A. We establish the necessity of the known sufficient condition for isometry of the map, namely that all Glimm ideals of A are primal. However, when the map is restricted to tensors with length bounded by a fixed quantity, a weaker necessary and sufficient condition is established. (c) 2005 Elsevier Inc. All rights reserved.

AB - We consider the natural contractive map from the central Haagerup, tensor product of a unital C*-algebra A with itself to the space of completely bounded maps CB(A) on A. We establish the necessity of the known sufficient condition for isometry of the map, namely that all Glimm ideals of A are primal. However, when the map is restricted to tensors with length bounded by a fixed quantity, a weaker necessary and sufficient condition is established. (c) 2005 Elsevier Inc. All rights reserved.

KW - Glimm ideal

KW - primal ideal

KW - matrix numerical range

KW - PRIMAL IDEALS

KW - STAR-ALGEBRAS

KW - MAPS

U2 - 10.1016/j.jfa.2005.03.006

DO - 10.1016/j.jfa.2005.03.006

M3 - Article

SN - 0022-1236

VL - 226

SP - 406

EP - 428

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

On the central Haagerup tensor product and completely bounded mappings of a C*-algebra

Abstract

Keywords

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