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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |