Quasi-Jordan Banach Algebras
We initiate a study of quasi-Jordan normed algebras. It is demonstrated that any quasi-Jordan Banach algebra with a norm 1 unit can be given an equivalent norm making the algebra isometrically isomorphic to a closed right ideal of a unital split quasi-Jordan Banach algebra; the set of invertible ele...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/690806 |
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| _version_ | 1832552399619751936 |
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| author | Reem K. Alhefthi Akhlaq A. Siddiqui Fatmah B. Jamjoom |
| author_facet | Reem K. Alhefthi Akhlaq A. Siddiqui Fatmah B. Jamjoom |
| author_sort | Reem K. Alhefthi |
| collection | DOAJ |
| description | We initiate a study of quasi-Jordan normed algebras. It is demonstrated that any quasi-Jordan Banach algebra with a norm 1 unit can be given an equivalent norm making the algebra isometrically isomorphic to a closed right ideal of a unital split quasi-Jordan Banach algebra; the set of invertible elements may not be open; the spectrum of any element is nonempty, but it may be neither bounded nor closed and hence not compact. Some characterizations of the unbounded spectrum of an element in a split quasi-Jordan Banach algebra with certain examples are given in the end. |
| format | Article |
| id | doaj-art-dec9513f15a1479a93df75345f1e17e1 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dec9513f15a1479a93df75345f1e17e12025-02-03T05:58:51ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/690806690806Quasi-Jordan Banach AlgebrasReem K. Alhefthi0Akhlaq A. Siddiqui1Fatmah B. Jamjoom2Department of Mathematics, College of Science, King Saud University, P.O. Box 2455-5, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455-5, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455-5, Riyadh 11451, Saudi ArabiaWe initiate a study of quasi-Jordan normed algebras. It is demonstrated that any quasi-Jordan Banach algebra with a norm 1 unit can be given an equivalent norm making the algebra isometrically isomorphic to a closed right ideal of a unital split quasi-Jordan Banach algebra; the set of invertible elements may not be open; the spectrum of any element is nonempty, but it may be neither bounded nor closed and hence not compact. Some characterizations of the unbounded spectrum of an element in a split quasi-Jordan Banach algebra with certain examples are given in the end.http://dx.doi.org/10.1155/2014/690806 |
| spellingShingle | Reem K. Alhefthi Akhlaq A. Siddiqui Fatmah B. Jamjoom Quasi-Jordan Banach Algebras Abstract and Applied Analysis |
| title | Quasi-Jordan Banach Algebras |
| title_full | Quasi-Jordan Banach Algebras |
| title_fullStr | Quasi-Jordan Banach Algebras |
| title_full_unstemmed | Quasi-Jordan Banach Algebras |
| title_short | Quasi-Jordan Banach Algebras |
| title_sort | quasi jordan banach algebras |
| url | http://dx.doi.org/10.1155/2014/690806 |
| work_keys_str_mv | AT reemkalhefthi quasijordanbanachalgebras AT akhlaqasiddiqui quasijordanbanachalgebras AT fatmahbjamjoom quasijordanbanachalgebras |