Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The topology on the primitive ideal space of transformation group $ C\sp{\ast} $-algebras and C.C.R. transformation group $ C\sp{\ast} $-algebras


Author: Dana P. Williams
Journal: Trans. Amer. Math. Soc. 266 (1981), 335-359
MSC: Primary 46L05; Secondary 22D25, 54H15
MathSciNet review: 617538
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ (G,\Omega )$ is a second countable transformation group and the stability groups are amenable then $ {C^ \ast }(G,\Omega )$ is C.C.R. if and only if the orbits are closed and the stability groups are C.C.R. In addition, partial results relating closed orbits to C.C.R. algebras are obtained in the nonseparable case.

In several cases, the topology of the primitive ideal space is calculated explicitly. In particular, if the stability groups are all contained in a fixed abelian subgroup $ H$, then the topology is computed in terms of $ H$ and the orbit structure, provided $ {C^ \ast }(G,\Omega )$ and $ {C^ \ast }(H,\Omega )$ are $ EH$-regular. These conditions are automatically met if $ G$ is abelian and $ (G,\Omega )$ is second countable.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L05, 22D25, 54H15

Retrieve articles in all journals with MSC: 46L05, 22D25, 54H15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0617538-7
PII: S 0002-9947(1981)0617538-7
Article copyright: © Copyright 1981 American Mathematical Society