Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups
Let S be a locally compact foundation semigroup with identity and be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of In this paper, we prove that X is invariantly complemented in if and only if the left ideal of has a bound...
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| Language: | English |
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University of Tehran
2014-03-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_50488_8bcf6c5a22fd9a2f7939bec5ecac6979.pdf |
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| author | B. Mohammadzadeh |
| author_facet | B. Mohammadzadeh |
| author_sort | B. Mohammadzadeh |
| collection | DOAJ |
| description | Let S be a locally compact foundation semigroup with identity and be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of In this paper, we prove that X is invariantly complemented in if and only if the left ideal of has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenable if and only if every complemented weak*-closed left translation invariant subspace of is invariantly complemented in . |
| format | Article |
| id | doaj-art-7836677b7eff4f6bbe334b4e4722e5f2 |
| institution | Kabale University |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2014-03-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-7836677b7eff4f6bbe334b4e4722e5f22025-08-20T03:53:51ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142014-03-01251515550488Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroupsB. Mohammadzadeh0Department of Mathematics, Faculty of Sciences, Babol University of Technology, Babol, Mazandaran, Islamic Republic of IranLet S be a locally compact foundation semigroup with identity and be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of In this paper, we prove that X is invariantly complemented in if and only if the left ideal of has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenable if and only if every complemented weak*-closed left translation invariant subspace of is invariantly complemented in .https://jsciences.ut.ac.ir/article_50488_8bcf6c5a22fd9a2f7939bec5ecac6979.pdfcomplemented subspacefoundation semigroupsemigroup algebras |
| spellingShingle | B. Mohammadzadeh Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups Journal of Sciences, Islamic Republic of Iran complemented subspace foundation semigroup semigroup algebras |
| title | Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups |
| title_full | Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups |
| title_fullStr | Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups |
| title_full_unstemmed | Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups |
| title_short | Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups |
| title_sort | weak closed invariant subspaces and ideals of semigroup algebras on foundation semigroups |
| topic | complemented subspace foundation semigroup semigroup algebras |
| url | https://jsciences.ut.ac.ir/article_50488_8bcf6c5a22fd9a2f7939bec5ecac6979.pdf |
| work_keys_str_mv | AT bmohammadzadeh weakclosedinvariantsubspacesandidealsofsemigroupalgebrasonfoundationsemigroups |