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Quasimultipliers on ð ¹ -Algebras

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  • Marjan Adib
  • Abdolhamid Riazi
  • Liaqat Ali Khan

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.

Suggested Citation

  • Marjan Adib & Abdolhamid Riazi & Liaqat Ali Khan, 2011. "Quasimultipliers on ð ¹ -Algebras," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-30, March.
    • Handle: RePEc:hin:jnlaaa:235273
    DOI: 10.1155/2011/235273
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