## Completely bounded mappings and simplicial complex structure in the primitive ideal space of a C*-algebra

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**Citation: **

*Robert J. Archbold, Douglas W. B. Somerset and Richard M. Timoney `Completely bounded mappings and simplicial complex structure in the primitive ideal space of a C*-algebra? in Transactions of the American Mathematical Society, 361, (3), 2009, pp 1397 - 1427*

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**Abstract: **

We consider the natural contraction from the central Haagerup
tensor product of a C*-algebra A with itself to the space of completely bounded
maps CB(A) on A and investigate those A where there exists an inverse
map with finite norm L(A). We show that a stabilised version L (A) =
supn L(Mn(A)) depends only on the primitive ideal space Prim(A). The
dependence is via simplicial complex structures (defined from primal intersections)
on finite sets of primitive ideals that contain a Glimm ideal of A.
Moreover L (A) = L(A ? K(H)), with K(H) the compact operators, which
requires us to develop the theory in the context of C*-algebras that are not
necessarily unital.

**Sponsor**

**Grant Number**

Science Foundation Ireland

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**Author's Homepage: **

http://people.tcd.ie/rtimoney
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**Description: **

PUBLISHED
**Author:**TIMONEY, RICHARD

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**Publisher: **

American Mathematical Society
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**Type of material: **

Journal Article#####
**Series/Report no: **

Transactions of the American Mathematical Society361

3

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**Availability: **

Full text available#####
**ISSN: **

1088-6850
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