Semigroup compactifications by generalized distal functions and a fixed point theorem
The notion of Semigroup compactification which is in a sense, a generalization of the classical Bohr (almost periodic) compactification of the usual additive reals R, has been studied by J. F. Berglund et. al. [2]. Their approach to the theory of semigroup compactification is based on the Gelfand-Na...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000285 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850230375070040064 |
|---|---|
| author | R. D. Pandian |
| author_facet | R. D. Pandian |
| author_sort | R. D. Pandian |
| collection | DOAJ |
| description | The notion of Semigroup compactification which is in a sense, a generalization of
the classical Bohr (almost periodic) compactification of the usual additive reals R,
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 commutative C* algebras,
where the spectra of admissible C*-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 semigroup S, and show that these function spaces are admissible C*-
subalgebras of C(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. |
| format | Article |
| id | doaj-art-293846f53477436da6fbd517e2cf39db |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-293846f53477436da6fbd517e2cf39db2025-08-20T02:03:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114225326010.1155/S0161171291000285Semigroup compactifications by generalized distal functions and a fixed point theoremR. D. Pandian0Department of Mathematics, North Central College, Naperville 60566, IL, USAThe notion of Semigroup compactification which is in a sense, a generalization of the classical Bohr (almost periodic) compactification of the usual additive reals R, 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 commutative C* algebras, where the spectra of admissible C*-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 semigroup S, and show that these function spaces are admissible C*- subalgebras of C(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.http://dx.doi.org/10.1155/S0161171291000285 |
| spellingShingle | R. D. Pandian Semigroup compactifications by generalized distal functions and a fixed point theorem International Journal of Mathematics and Mathematical Sciences |
| title | Semigroup compactifications by generalized distal functions and a fixed point theorem |
| title_full | Semigroup compactifications by generalized distal functions and a fixed point theorem |
| title_fullStr | Semigroup compactifications by generalized distal functions and a fixed point theorem |
| title_full_unstemmed | Semigroup compactifications by generalized distal functions and a fixed point theorem |
| title_short | Semigroup compactifications by generalized distal functions and a fixed point theorem |
| title_sort | semigroup compactifications by generalized distal functions and a fixed point theorem |
| url | http://dx.doi.org/10.1155/S0161171291000285 |
| work_keys_str_mv | AT rdpandian semigroupcompactificationsbygeneralizeddistalfunctionsandafixedpointtheorem |