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

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 → …

Fingerprint

Multiplier Algebra
Algebra
Extremally Disconnected
Primitive Ideal
Limit Set
Prime Ideal
Locally Compact
Homeomorphism
Unital
C*-algebra
Ring
Closed

Keywords

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

Cite this

Archbold, R. J., & Somerset, D. W. B. (2015). Minimal Primal Ideals in the Multiplier Algebra of a C0(X)-algebra. In W. Arendt, R. Chill, & Y. Tomilov (Eds.), Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics (pp. 17-29). (Operator Theory: Advances and Applications; Vol. 250). Springer . https://doi.org/10.1007/978-3-319-18494-4_2

Minimal Primal Ideals in the Multiplier Algebra of a C0(X)-algebra. / Archbold, R. J.; Somerset, D. W. B.

Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics. ed. / Wolfgang Arendt; Ralph Chill; Yuri Tomilov. Springer , 2015. p. 17-29 (Operator Theory: Advances and Applications; Vol. 250).

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

Archbold, RJ & Somerset, DWB 2015, Minimal Primal Ideals in the Multiplier Algebra of a C0(X)-algebra. in W Arendt, R Chill & Y Tomilov (eds), Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics. Operator Theory: Advances and Applications, vol. 250, Springer , pp. 17-29, Conference on Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, Herrenhut, Germany, 1/06/13. https://doi.org/10.1007/978-3-319-18494-4_2
Archbold RJ, Somerset DWB. Minimal Primal Ideals in the Multiplier Algebra of a C0(X)-algebra. In Arendt W, Chill R, Tomilov Y, editors, Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics. Springer . 2015. p. 17-29. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-319-18494-4_2
Archbold, R. J. ; Somerset, D. W. B. / Minimal Primal Ideals in the Multiplier Algebra of a C0(X)-algebra. Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics. editor / Wolfgang Arendt ; Ralph Chill ; Yuri Tomilov. Springer , 2015. pp. 17-29 (Operator Theory: Advances and Applications).
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