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Modules over operator algebras and its module maps. (English) Zbl 0893.46040

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
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