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Inner invariant means
and conjugation operators


Author: Yuji Takahashi
Journal: Proc. Amer. Math. Soc. 124 (1996), 193-196
MSC (1991): Primary 43A07, 43A15
DOI: https://doi.org/10.1090/S0002-9939-96-03201-7
MathSciNet review: 1307568
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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 [Enhancements On Off] (What's this?)

  • 1 E. G. Effros, Property $\Gamma$ 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
  • 5 V. Losert and H. Rindler, Asymptotically central functions and invariant extensions of Dirac measure, Proc. Conf. Probability Measures on Groups VII (Oberwolfach, 1983), Lecture Notes in Math., vol. 1064, Springer, Berlin and New York, 1984, 368--378. MR 86e:43007
  • 6 ------, 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
  • 9 J. P. Pier, Amenable locally compact groups, Wiley, New York, 1984. MR 86a:43001
  • 10 C. K. Yuan, The existence of inner invariant means on $L^\infty(G)$, 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: https://doi.org/10.1090/S0002-9939-96-03201-7
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
Article copyright: © Copyright 1996 American Mathematical Society

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