Abstract
Given an essential ideal \(J\subset A\) of a \(C^*\) -algebra \(A\) and a Hilbert \(C^*\) -module \(M\) over \(A\) , we place \(M\) between two other Hilbert \(C^*\) -modules over \(A\) , \(M_J\subset M\subset M^J\) , in such a way that every submodule here is thick, i.e., its orthogonal complement in the greater module is trivial. We introduce the class \(\mathbb B_J(M)\) of \(J\) -adjointable operators on a Hilbert \(C^*\) -module \(M\) over \(A\) and prove that this class isometrically embeds in the \(C^*\) -algebras of all adjointable operators both of \(M_J\) and of \(M^J\) .
DOI 10.1134/S1061920824601782
