Quasimultipliers on 𝐹-Algebras
We investigate the extent to which the study of quasimultipliers can be made beyond Banach algebras. We will focus mainly on the class of 𝐹-algebras, in particular on complete 𝑘-normed algebras, 0<𝑘≤1, not necessarily locally convex. We include a few counterexamples to demonstrate that some of ou...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/235273 |
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| author | Marjan Adib Abdolhamid Riazi Liaqat Ali Khan |
| author_facet | Marjan Adib Abdolhamid Riazi Liaqat Ali Khan |
| author_sort | Marjan Adib |
| collection | DOAJ |
| description | We investigate the extent to which the study of quasimultipliers
can be made beyond Banach algebras. We will focus mainly on the class of 𝐹-algebras, in particular on complete 𝑘-normed algebras, 0<𝑘≤1, not necessarily
locally convex. We include a few counterexamples to demonstrate that some of
our results do not carry over to general 𝐹-algebras. The bilinearity and joint continuity of quasimultipliers on an 𝐹-algebra 𝐴 are obtained under the assumption of strong factorability. Further, we establish several properties of the strict and
quasistrict topologies on the algebra 𝑄𝑀(𝐴) of quasimultipliers of a complete
𝑘-normed algebra 𝐴 having a minimal ultra-approximate identity. |
| format | Article |
| id | doaj-art-706f2fdd9bde4b0c865b17c3347a8b91 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-706f2fdd9bde4b0c865b17c3347a8b912025-02-03T01:21:18ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/235273235273Quasimultipliers on 𝐹-AlgebrasMarjan Adib0Abdolhamid Riazi1Liaqat Ali Khan2Department of Mathematics, Payamenoor University-Aligodarz Branch, Aligodarz, IranDepartment of Mathematics and Computer Science, Amirkabir University of Technology, P.O. Box 15914, Tehran, IranDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe investigate the extent to which the study of quasimultipliers can be made beyond Banach algebras. We will focus mainly on the class of 𝐹-algebras, in particular on complete 𝑘-normed algebras, 0<𝑘≤1, not necessarily locally convex. We include a few counterexamples to demonstrate that some of our results do not carry over to general 𝐹-algebras. The bilinearity and joint continuity of quasimultipliers on an 𝐹-algebra 𝐴 are obtained under the assumption of strong factorability. Further, we establish several properties of the strict and quasistrict topologies on the algebra 𝑄𝑀(𝐴) of quasimultipliers of a complete 𝑘-normed algebra 𝐴 having a minimal ultra-approximate identity.http://dx.doi.org/10.1155/2011/235273 |
| spellingShingle | Marjan Adib Abdolhamid Riazi Liaqat Ali Khan Quasimultipliers on 𝐹-Algebras Abstract and Applied Analysis |
| title | Quasimultipliers on 𝐹-Algebras |
| title_full | Quasimultipliers on 𝐹-Algebras |
| title_fullStr | Quasimultipliers on 𝐹-Algebras |
| title_full_unstemmed | Quasimultipliers on 𝐹-Algebras |
| title_short | Quasimultipliers on 𝐹-Algebras |
| title_sort | quasimultipliers on 𝐹 algebras |
| url | http://dx.doi.org/10.1155/2011/235273 |
| work_keys_str_mv | AT marjanadib quasimultipliersonfalgebras AT abdolhamidriazi quasimultipliersonfalgebras AT liaqatalikhan quasimultipliersonfalgebras |