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Paper IPM / M / 15242  


Abstract:  
In this paper, we deal with some fixed point properties for a
semitopological semigroup S acting on a compact convex subset K of a Banach space. We first focus on the space LMC(S) of left multiplicatively continuous functions on S and its strong left amenability; the existence of a compact left ideal group in the
LMCcompactification of S. We then study the relation between left amenability and strong left amenability of LMC(S) with a common fixed point property for nonexpansive and asymptotically nonexpansive actions of S. Our results improve a result of T. Mitchell in 1970, and answer an open problem of A.T.M. Lau in 2010 for the class of strongly left amenable semitopological semigroups.
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