On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras
In this paper, we investigate the existence of an ultra central approximate identity for a Banach algebra A and its second dual A∗∗. Also, we prove that for a left cancellative regular semigroup S, ℓ1S∗∗ has an ultra central approximate identity if and only if S is a group. As an application, we sho...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9527678 |
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| _version_ | 1832549050646265856 |
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| author | Amir Sahami Seyedeh Fatemeh Shariati |
| author_facet | Amir Sahami Seyedeh Fatemeh Shariati |
| author_sort | Amir Sahami |
| collection | DOAJ |
| description | In this paper, we investigate the existence of an ultra central approximate identity for a Banach algebra A and its second dual A∗∗. Also, we prove that for a left cancellative regular semigroup S, ℓ1S∗∗ has an ultra central approximate identity if and only if S is a group. As an application, we show that for a left cancellative semigroup S, ℓ1S∗∗ is pseudo-contractible if and only if S is a finite group. We also study this property for φ-Lau product Banach algebras and the module extension Banach algebras. |
| format | Article |
| id | doaj-art-9c18e86a88c84ec38fe12c7017ce98e3 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9c18e86a88c84ec38fe12c7017ce98e32025-02-03T06:12:24ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9527678On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup AlgebrasAmir Sahami0Seyedeh Fatemeh Shariati1Department of Mathematics Faculty of Basic ScienceDepartment of Mathematics and Computer ScienceIn this paper, we investigate the existence of an ultra central approximate identity for a Banach algebra A and its second dual A∗∗. Also, we prove that for a left cancellative regular semigroup S, ℓ1S∗∗ has an ultra central approximate identity if and only if S is a group. As an application, we show that for a left cancellative semigroup S, ℓ1S∗∗ is pseudo-contractible if and only if S is a finite group. We also study this property for φ-Lau product Banach algebras and the module extension Banach algebras.http://dx.doi.org/10.1155/2022/9527678 |
| spellingShingle | Amir Sahami Seyedeh Fatemeh Shariati On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras Journal of Mathematics |
| title | On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras |
| title_full | On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras |
| title_fullStr | On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras |
| title_full_unstemmed | On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras |
| title_short | On Pseudo-contractibility and Ultra Central Approximate Identity of Some Semigroup Algebras |
| title_sort | on pseudo contractibility and ultra central approximate identity of some semigroup algebras |
| url | http://dx.doi.org/10.1155/2022/9527678 |
| work_keys_str_mv | AT amirsahami onpseudocontractibilityandultracentralapproximateidentityofsomesemigroupalgebras AT seyedehfatemehshariati onpseudocontractibilityandultracentralapproximateidentityofsomesemigroupalgebras |