On transformation group -algebras with continuous trace

Author:
Siegfried Echterhoff

Journal:
Trans. Amer. Math. Soc. **343** (1994), 117-133

MSC:
Primary 46L55; Secondary 22D25, 54H20

DOI:
https://doi.org/10.1090/S0002-9947-1994-1157612-1

MathSciNet review:
1157612

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we answer some questions posed by Dana Williams in [19] concerning the problem under which conditions the transformation group -algebra of a locally compact transformation group (*G*, ) has continuous trace. One consequence will be, for compact *G*, that has continuous trace if and only if the stabilizer map is continuous. We also give a complete solution to the problem if *G* is discrete.

**[1]**L. W. Baggett,*A description of the topology on the dual spaces of certain locally compact groups*, Trans. Amer. Math. Soc.**132**(1968), 175-215. MR**0409720 (53:13472)****[2]**L. Baggett and T. Sund,*The Hausdorff dual problem for connected groups*, J. Funct. Anal.**43**(1981), 60-68. MR**639797 (83a:22006)****[3]**J. Dixmier, -*algebras*, North-Holland Math. Library, 1977. MR**0458185 (56:16388)****[4]**S. Echterhoff,*The primitive ideal space of twisted covariant systems with continuously varying stabilizers*, Math. Ann.**292**(1992), 59-84. MR**1141785 (93a:46128)****[5]**-,*Regularizations of twisted covariant systems and crossed products with continuous trace*, J. Funct. Anal.**116**(1993), 277-313. MR**1239073 (95c:46112)****[6]**S. Echterhoff and E. Kaniuth,*Certain group extensions and twisted covariance algebras with generalized continuous trace*, Lecture Notes in Math., Berlin, Heidelberg, and New York, 1987, pp. 159-169. MR**974312 (90c:46083)****[7]**J. M. G. Fell,*A Hausdorff topology on the closed subsets of a locally compact non-Hausdorff space*, Proc. Amer. Math. Soc.**13**(1962) 472-476. MR**0139135 (25:2573)****[8]**-,*The structure of algebras of operator fields*, Acta Math.**106**(1962) 237-268. MR**0164248 (29:1547)****[9]**-,*Weak containment and induced representations of groups*. II, Trans. Amer. Math. Soc.**110**(1964), 424-447. MR**0159898 (28:3114)****[10]**J. Glimm,*Families of induced representations*, Pacific J. Math.**12**(1962) 885-911. MR**0146297 (26:3819)****[11]**F. P. Greenleaf,*Amenable actions of locally compact groups*, J. Funct. Anal.**4**(1969), 295-315. MR**0246999 (40:268)****[12]**R. W. Henrichs,*Die Frobeniuseigenschaft für diskrete Gruppen*, Math. Z.**147**(1976,) 191-199. MR**0404522 (53:8324)****[13]**E. Kaniuth,*Primitive ideal spaces of groups with relative compact conjugacy classes*, Arch. Math.**32**(1979), 16-24. MR**532844 (81f:22009)****[14]**-,*On topological Frobenius reciprocity for locally compact groups*, Arch. Math.**48**(1987), 286-297. MR**884559 (89d:22002)****[15]**D. Montgomery and L. Zippin,*Topological transformation groups*, Interscience, New York, 1955. MR**0073104 (17:383b)****[16]**I. Raeburn and D. P. Williams,*Crossed products by actions which are locally unitary on the stabilizers*, J. Funct. Anal.**81**(1988), 385-431. MR**971886 (91c:46093)****[17]**E. Thoma,*Eine Charakterisierung diskreter Gruppen vom Typ*I, Invent. Math.**6**(1968), 190-196. MR**0248288 (40:1540)****[18]**D. P. Williams,*The topology on the primitive ideal space of transformation group*-*algebras and C.C.R transformation group*-*algebras*, Trans. Amer. Math. Soc.**266**(1981), 335-359. MR**617538 (82h:46081)****[19]**-,*Transformation group*-*algebras with continuous trace*, J. Funct. Anal.**41**(1981), 40-76. MR**614226 (83c:46066)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1157612-1

Keywords:
-algebra,
transformation group,
continuous trace,
subgroup algebra

Article copyright:
© Copyright 1994
American Mathematical Society