2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100923We present a short and elegant proof of the complete theory of strict representations of the algebra B^a(E) of all adjointable operators on a Hilbert B-module E by operators on a Hilbert C-module F. Aanalogue for W*-modules and normal representations is also proved. As an application we furnish a new proof of Blecher's Eilenberg-Watts theorem.Publication data added, corrected an ambiguity in the formulation of Corollary 1.20 (present also in the published version) and adjusted the proof appropriatelyOperator Algebras46L08; 46L55; 46L53; 46M05; 46M15text