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Inner invariant means and conjugation operators
Author(s):
Yuji
Takahashi
Journal:
Proc. Amer. Math. Soc.
124
(1996),
193-196.
MSC (1991):
Primary 43A07, 43A15
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Abstract:
It is shown that Paschke's result cannot be generalized to the [IN]-group setting given by Lau and Paterson. This resolves negatively a problem raised by Lau and Paterson.
References:
- 1
- E. G. Effros, Property
and inner amenability, Proc. Amer. Math. Soc. 47 (1975), 483--486. MR 50:8100 - 2
- F. P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand, New York, 1969. MR 40:4776
- 3
- A. T. M. Lau and A. L. T. Paterson, Operator theoretic characterizations of [IN]-groups and inner amenability, Proc. Amer. Math. Soc. 102 (1988), 893--897. MR 89f:43003
- 4
- ------, Inner amenable locally compact groups, Trans. Amer. Math. Soc. 325 (1991), 155--169. MR 91h:43002
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- ------, Conjugation-invariant means, Colloq. Math. 51 (1987), 221--225. MR 89d:43001
- 7
- W. L. Paschke, Inner amenability and conjugation operators, Proc. Amer. Math. Soc. 71 (1978), 117--118. MR 57:13508
- 8
- A. L. T. Paterson, Amenability, Math. Surveys Monographs, vol. 29, Amer. Math. Soc., Providence, RI, 1988. MR 90e:43001
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- 10
- C. K. Yuan, The existence of inner invariant means on
, J. Math. Anal. Appl. 130 (1988), 514--524. MR 89g:43001
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Additional Information:
Yuji
Takahashi
Affiliation:
Department of Mathematics, Hokkaido University of Education, Hakodate, Hachiman-cho, Hakodate, 040 Japan
Email:
ytakahas@hak.hokkyodai.ac.jp
DOI:
10.1090/S0002-9939-96-03201-7
PII:
S 0002-9939(96)03201-7
Keywords:
[IN]-groups,
inner invariant means,
amenability,
free groups,
$C^*$-algebras
Received by editor(s):
July 29, 1994
Dedicated:
Dedicated to Professor Satoru Igari on his sixtieth birthday
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1996,
American Mathematical Society
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