Minimal Primal Ideals in the Multiplier Algebra of a C0(X)-algebra

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Let A be a stable, sigma-unital, continuous C-0(X)-algebra with surjective base map phi : Prim(A) -> X, where Prim(A) is the primitive ideal space of the C*-algebra A. Suppose that phi(-1) (x) is contained in a limit set in Prim(A) for each x is an element of X (so that A is quasi-standard). Let C-R(X) be the ring of continuous real-valued functions on X. It is shown that there is a homeomorphism between the space of minimal prime ideals of C-R(X) and the space MinPrimal(M(A)) of minimal closed primal ideals of the multiplier algebra M(A). If A is separable then MinPrimal(M(A)) is compact and extremally disconnected but if X = beta N \ N then MinPrimal(M(A)) is nowhere locally compact.

Original languageEnglish
Title of host publicationOperator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics
EditorsWolfgang Arendt, Ralph Chill, Yuri Tomilov
PublisherSpringer
Pages17-29
Number of pages13
ISBN (Electronic)978-3-319-18494-4
ISBN (Print)978-3-319-18493-7
DOIs
Publication statusPublished - 2015
EventConference on Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics - Herrenhut, Germany
Duration: 1 Jun 2013 → …

Publication series

NameOperator Theory: Advances and Applications
PublisherBirkhäuser Basel
Volume250
ISSN (Print)0255-0156
ISSN (Electronic)0255-0156

Conference

ConferenceConference on Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics
CountryGermany
CityHerrenhut
Period1/06/13 → …

Keywords

  • C∗-algebra
  • C0(X)-algebra
  • multiplier algebra
  • minimal prime ideal
  • minimal primal ideal
  • primitive ideal space
  • quasi standard

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