TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY
In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S)...
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| Format: | Article |
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| Language: | English |
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University of Tehran
2002-12-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31638_bd7b842b5687cd4d8c4a7ccca3aaeb40.pdf |
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| collection | DOAJ |
| description | In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. The main purpose of this paper is to prove a topological analogue (which is also a generalization) of this theorem for locally compact semigroups. |
| format | Article |
| id | doaj-art-c0286aaa2fbd4f1e8f6c34a0ec807cfe |
| institution | OA Journals |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2002-12-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-c0286aaa2fbd4f1e8f6c34a0ec807cfe2025-08-20T02:25:51ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142002-12-0113431638TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITYIn this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. The main purpose of this paper is to prove a topological analogue (which is also a generalization) of this theorem for locally compact semigroups.https://jsciences.ut.ac.ir/article_31638_bd7b842b5687cd4d8c4a7ccca3aaeb40.pdf |
| spellingShingle | TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY Journal of Sciences, Islamic Republic of Iran |
| title | TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY |
| title_full | TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY |
| title_fullStr | TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY |
| title_full_unstemmed | TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY |
| title_short | TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY |
| title_sort | topologically stationary locally compact semigroup and amenability |
| url | https://jsciences.ut.ac.ir/article_31638_bd7b842b5687cd4d8c4a7ccca3aaeb40.pdf |