\(\varphi\)-multipliers on Banach algebras and topological modules. (English) Zbl 1350.46035

Summary: We prove some results concerning Arens regularity and amenability of the Banach algebra \(M_\varphi (A)\) of all \(\varphi\)-multipliers on a given Banach algebra \(A\). We also consider \(\varphi\)-multipliers in the general topological module setting and investigate some of their properties. We discuss the \(\varphi\)-strict and \(\varphi\)-uniform topologies on \(M_\varphi (A)\). A characterization of \(\varphi\)-multipliers on \(L_1 (G)\)-module \(L_p (G)\), where \(G\) is a compact group, is given.


46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47B48 Linear operators on Banach algebras
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