Ideals in the multiplier and corona algebras of a Co(X)-algebra

R. J. Archbold, D. W. B. Somerset

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let A be a stable, σ-unital C*-algebra which is a C0(X)-algebra, that is, for which there is a continuous map ϕ from Prim(A), the primitive ideal space of A with the hull-kernel topology, to the locally compact Hausdorff space X. We show that there is an injective map L from the lattice of z-ideals of the ring of continuous functions on the completely regular space Im(ϕ) to the lattice of closed ideals of M(A), the multiplier algebra of A. For any two ideals in the range of L, there is a maximal ideal of M(A) containing one but not the other. If Im(ϕ) is infinite, then the corona algebra M(A)/A has at least 2c maximal ideals.
Original languageEnglish
Pages (from-to)365-381
Number of pages17
JournalJournal of the London Mathematical Society
Volume85
Issue number2
Early online date26 Jan 2012
DOIs
Publication statusPublished - Apr 2012

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Corona
Maximal Ideal
Multiplier
Rings of Continuous Functions
Multiplier Algebra
Primitive Ideal
Closed Ideals
Algebra
Compact Hausdorff Space
Continuous Map
Locally Compact
Unital
Injective
C*-algebra
kernel
Topology
Range of data

Cite this

Ideals in the multiplier and corona algebras of a Co(X)-algebra. / Archbold, R. J.; Somerset, D. W. B.

In: Journal of the London Mathematical Society, Vol. 85, No. 2, 04.2012, p. 365-381.

Research output: Contribution to journalArticle

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