Weak* fixed point property and asymptotic centre for the Fourier-Stieltjes algebra of a locally compact group
In this paper we show that the Fourier-Stieltjes algebra B(G) of a non-compact locally compact group G cannot have the weak* fixed point property for nonexpansive mappings. This answers two open problems posed at a conference in Marseille-Luminy in 1989. We also show that a locally compact group is...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1 January 2013
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| In: |
Journal of functional analysis
Year: 2012, Volume: 264, Issue: 1, Pages: 288-302 |
| ISSN: | 1096-0783 |
| DOI: | 10.1016/j.jfa.2012.10.011 |
| Online Access: | Verlag, kostenfrei, Volltext: http://dx.doi.org/10.1016/j.jfa.2012.10.011 Verlag, kostenfrei, Volltext: http://www.sciencedirect.com/science/article/pii/S0022123612003862 
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| Author Notes: | Gero Fendler, Anthony To-Ming Lau, Michael Leinert |
| Summary: | In this paper we show that the Fourier-Stieltjes algebra B(G) of a non-compact locally compact group G cannot have the weak* fixed point property for nonexpansive mappings. This answers two open problems posed at a conference in Marseille-Luminy in 1989. We also show that a locally compact group is compact exactly if the asymptotic centre of any non-empty weak* closed bounded convex subset C in B(G) with respect to a decreasing net of bounded subsets is a non-empty norm compact subset. In particular, when G is compact, B(G) has the weak* fixed point property for left reversible semigroups. This generalizes a classical result of T.C. Lim for the circle group. As a consequence of our main results we obtain that a number of properties, some of which were known to hold for compact groups, in fact characterize compact groups. |
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| Item Description: | Available online 7 November 2012 Gesehen am 06.06.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1096-0783 |
| DOI: | 10.1016/j.jfa.2012.10.011 |