Publication Date:
1991-01-01
Description:
The notion of Semigroup compactification which is in a sense, a generalization of the classical Bohr (almost periodic) compactification of the usual additive realsR, has been studied by J. F. Berglund et. al. [2]. Their approach to the theory of semigroup compactification is based on the Gelfand-Naimark theory of commutativeC*algebras, where the spectra of admissibleC*-algebras, are the semigroup compactifications. H. D. Junghenn's extensive study of distal functions is from the point of view of semigroup compactifications [5]. In this paper, extending Junghenn's work, we generalize the notion of distal flows and distal functions on an arbitrary semitopological semigroupS, and show that these function spaces are admissibleC*- subalgebras ofC(S). We then characterize their spectra (semigroup compactifications) in terms of the universal mapping properties these compactifications enjoy. In our work, as it is in Junghenn's, the Ellis semigroup plays an important role. Also, relating the existence of left invariant means on these algebras to the existence of fixed points of certain affine flows, we prove the related fixed point theorem.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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