Argün, Ziya; Rowlands, K. On quasi-multipliers. (English) Zbl 0824.46053 Stud. Math. 108, No. 3, 217-245 (1994). Summary: A quasi-multiplier is a generalization of the notion of a left (right, double) multiplier. The first systematic account of the general theory of quasi-multipliers on a Banach algebra with a bounded approximate identity was given in a paper by McKennon in 1977. Further developments have been made in more recent papers by Vasudevan and Goel, Kassem and Rowlands, and Lin.In this paper, we consider the quasi-multipliers of algebras not hitherto considered in the literature. In particular, we study the quasi- multipliers of \(A^*\)-algebras, of the algebra of compact operators on a Banach space, and of the Pedersen ideal of a \(C^*\)-algebra. We also consider the strict topology on the quasi-multiplier space \(QM(A)\) of a Banach algebra \(A\) with a bounded approximate identity. We prove that, if \(M_ \ell(A)\) (resp. \(M_ r(A)\)) denotes the algebra of left (right) multipliers on \(A\), then \(M_ \ell(A)+ M_ r(A)\) is strictly dense in \(QM(A)\), thereby generalizing a theorem due to Lin. Cited in 8 Documents MSC: 46H05 General theory of topological algebras Keywords:quasi-multipliers; \(A^*\)-algebras; Pedersen ideal of a \(C^*\)-algebra; strict topology PDFBibTeX XMLCite \textit{Z. Argün} and \textit{K. Rowlands}, Stud. Math. 108, No. 3, 217--245 (1994; Zbl 0824.46053) Full Text: DOI EuDML