Restricting operators to thick Hilbert C*-submodules

Given an essential ideal J 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, MJ M MJ, in such a way that each submodule here is thick, i. e. its orthogonal conmplement in the greater module is trivial. We introduce the class BJ (M) of J-adjointable operators on a Hilbert C*-module M over A, and prove that this class isometrically embeds into the C*-algebras of all adjointable operators both of MJ and of MJ.