Quasimultipliers on ð ¹ -Algebras

Marjan Adib, Abdolhamid Riazi and Liaqat Ali Khan

Abstract and Applied Analysis, 2011, vol. 2011, 1-30

Abstract:

We investigate the extent to which the study of quasimultipliers can be made beyond Banach algebras. We will focus mainly on the class of ð ¹ -algebras, in particular on complete 𠑘 -normed algebras, 0 < 𠑘 ≤ 1 , not necessarily locally convex. We include a few counterexamples to demonstrate that some of our results do not carry over to general ð ¹ -algebras. The bilinearity and joint continuity of quasimultipliers on an ð ¹ -algebra ð ´ are obtained under the assumption of strong factorability. Further, we establish several properties of the strict and quasistrict topologies on the algebra ð ‘„ ð ‘€ ( ð ´ ) of quasimultipliers of a complete 𠑘 -normed algebra ð ´ having a minimal ultra-approximate identity.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:235273

DOI: 10.1155/2011/235273

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