Completely bounded mappings and simplicial complex structure in the primitive ideal space of a C*-algebra
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 - 1427Download Item:
2009-ArchSomTim-TAMS.pdf (published (publisher copy) peer-reviewed) 393.4Kb
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
Author's Homepage:
http://people.tcd.ie/rtimoneyDescription:
PUBLISHED
Author: TIMONEY, RICHARD
Publisher:
American Mathematical SocietyType of material:
Journal ArticleSeries/Report no:
Transactions of the American Mathematical Society361
3
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Full text availableISSN:
1088-6850Licences: