Xu, Tianzhou Modules over operator algebras and its module maps. (English) Zbl 0893.46040 Northeast. Math. J. 13, No. 1, 107-114 (1997). Summary: Let \(A\) and \(B\) be Banach algebras, \(X\) a Banach \(AB\)-bimodule, and \(M(X)\) the space of all \(A\)-\(B\)-bimodule maps from \(AB\) to \(X\). We introduce a locally convex topology \(\mu\) on the space \(M(X)\) and investigate some of the properties of \((M(X),\mu)\). Moreover, we characterize the equicontinuous subsets of \((M(X),\mu)^*\) when \(A\) and \(B\) are \(C^*\)-algebras. MSC: 46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46L05 General theory of \(C^*\)-algebras Keywords:module map; dual space; operator algebra; Banach algebras; Banach \(AB\)-bimodule; space of all \(A\)-\(B\)-bimodule maps; locally convex topology; equicontinuous subsets; \(C^*\)-algebras PDFBibTeX XMLCite \textit{T. Xu}, Northeast. Math. J. 13, No. 1, 107--114 (1997; Zbl 0893.46040)