Bounded Approximate Identities in Ternary Banach Algebras
Let A be a ternary Banach algebra. We prove that if A has a left-bounded approximating set, then A has a left-bounded approximate identity. Moreover, we show that if A has bounded left and right approximate identities, then A has a bounded approximate identity. Hence, we prove Altman’s Theorem and D...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/386785 |
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| author | Madjid Eshaghi Gordji Ali Jabbari Gwang Hui Kim |
| author_facet | Madjid Eshaghi Gordji Ali Jabbari Gwang Hui Kim |
| author_sort | Madjid Eshaghi Gordji |
| collection | DOAJ |
| description | Let A be a ternary Banach algebra. We prove that if A has a left-bounded approximating set, then A has a left-bounded approximate identity. Moreover, we show that if A has bounded left and right approximate identities, then A has a bounded approximate identity. Hence, we prove Altman’s Theorem and Dixon’s Theorem for ternary Banach algebras. |
| format | Article |
| id | doaj-art-50770a05169948dfabab8ddc3f224448 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-50770a05169948dfabab8ddc3f2244482025-02-03T01:32:03ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/386785386785Bounded Approximate Identities in Ternary Banach AlgebrasMadjid Eshaghi Gordji0Ali Jabbari1Gwang Hui Kim2Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranYoung Researchers Club, Ardabil Branch, Islamic Azad University, P.O. Box 15655-461, Ardabil, IranDepartment of Mathematics, Kangnam University, Youngin, Gyeonggi 446-702, Republic of KoreaLet A be a ternary Banach algebra. We prove that if A has a left-bounded approximating set, then A has a left-bounded approximate identity. Moreover, we show that if A has bounded left and right approximate identities, then A has a bounded approximate identity. Hence, we prove Altman’s Theorem and Dixon’s Theorem for ternary Banach algebras.http://dx.doi.org/10.1155/2012/386785 |
| spellingShingle | Madjid Eshaghi Gordji Ali Jabbari Gwang Hui Kim Bounded Approximate Identities in Ternary Banach Algebras Abstract and Applied Analysis |
| title | Bounded Approximate Identities in Ternary Banach Algebras |
| title_full | Bounded Approximate Identities in Ternary Banach Algebras |
| title_fullStr | Bounded Approximate Identities in Ternary Banach Algebras |
| title_full_unstemmed | Bounded Approximate Identities in Ternary Banach Algebras |
| title_short | Bounded Approximate Identities in Ternary Banach Algebras |
| title_sort | bounded approximate identities in ternary banach algebras |
| url | http://dx.doi.org/10.1155/2012/386785 |
| work_keys_str_mv | AT madjideshaghigordji boundedapproximateidentitiesinternarybanachalgebras AT alijabbari boundedapproximateidentitiesinternarybanachalgebras AT gwanghuikim boundedapproximateidentitiesinternarybanachalgebras |