Bounded Approximate Identities in Ternary Banach Algebras

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...

Full description

Bibliographic Details
Main Authors: Madjid Eshaghi Gordji, Ali Jabbari, Gwang Hui Kim
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/386785
id doaj-50770a05169948dfabab8ddc3f224448
record_format Article
spelling doaj-50770a05169948dfabab8ddc3f2244482020-11-24T23:26:29ZengHindawi LimitedAbstract 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
collection DOAJ
language English
format Article
sources DOAJ
author Madjid Eshaghi Gordji
Ali Jabbari
Gwang Hui Kim
spellingShingle Madjid Eshaghi Gordji
Ali Jabbari
Gwang Hui Kim
Bounded Approximate Identities in Ternary Banach Algebras
Abstract and Applied Analysis
author_facet Madjid Eshaghi Gordji
Ali Jabbari
Gwang Hui Kim
author_sort Madjid Eshaghi Gordji
title Bounded Approximate Identities in Ternary Banach Algebras
title_short 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_sort bounded approximate identities in ternary banach algebras
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
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.
url http://dx.doi.org/10.1155/2012/386785
work_keys_str_mv AT madjideshaghigordji boundedapproximateidentitiesinternarybanachalgebras
AT alijabbari boundedapproximateidentitiesinternarybanachalgebras
AT gwanghuikim boundedapproximateidentitiesinternarybanachalgebras
_version_ 1725554968787681280

Similar Items