fixed point property and asymptotic centre for the Fourier-Stieltjes algebra of a locally compact group

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• 作者：Gero Fendler^a ; ^{gero.fendler@univie.ac.at} ; Anthony To-Ming Lau^b ; ¹ ; ^{tlau@math.ualberta.ca} ; Michael Leinert^c ; ^{leinert@math.uni-heidelberg.de}
• 关键词：Weak?-fixed point property ; Fourier&ndash ; Stieltjes algebra ; Compact groups ; Asymptotic centre ; Left reversible semigroups ; Fell group
• 刊名：Journal of Functional Analysis
• 出版年：2013
• 出版时间：1 January, 2013
• 年：2013
• 卷：264
• 期：1
• 页码：288-302
• 全文大小：203 K

文摘

In this paper we show that the Fourier-Stieltjes algebra of a non-compact locally compact group G cannot have the 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 closed bounded convex subset C in with respect to a decreasing net of bounded subsets is a non-empty norm compact subset. In particular, when G is compact, has the 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.