Frames of multipliers in tensor products of Hilbert modules over pro-\(C^{*}\)-algebras
\textit{M.\,Frank} and \textit{D.\,Larson} [Contemp.\ Math.\ 247, 207--233 (1999; Zbl 0949.46027)] generalized the notion of frame to the setting of Hilbert \(C^*\)-modules. \textit{I.\,Raeburn} and \textit{S.\,J.\thinspace Thompson} [Proc.\ Am.\ Math.\ Soc.\ 131, No.\,5, 1557--1564 (2003; Zbl 1015.46034)] introduced the notion of standard frame of multipliers for a Hilbert \(C^*\)-module. In the paper under review, the author extends a result of \textit{A.\,Khosravi} and \textit{B.\,Khosravi} [Proc.\ Indian Acad.\ Sci., Math.\ Sci.\ 117, No.\,1, 1--12 (2007; Zbl 1125.46048)] for standard frames of multipliers. For a standard frame of multipliers for a Hilbert \(A\)-module \(E\) and a standard frame of multipliers for a Hilbert \(B\)-module \(F\), she constructs a standard frame of multipliers for the external tensor product of \(E\) and \(F\) and for the inner tensor product of \(E\) and \(F\), using a nondegenerate pro-\(C^*\)-morphism from \(A\) to the pro-\(C^*\)-algebra of all adjointable module morphisms on \(F\).
scientific article; zbMATH DE number 5706223
scientific article