Resumen de Extensions of Hilbert C*-modules
Boris Guljas, Damir Bakic
Let V be a full Hilbert C*-module over a non unital C*-algebra. Denote by Vd the Hilbert C*-module over the multiplier algebra M(A) consisting of all adjointable maps from A to V. Then V can be naturally embedded in Vd as an ideal submodule and restriction to V gives an isomorphism of C*-algebras of adjointable operators on Vd and on V. The extended module Vd is the completion of V with respect to a variant of strict topology and serves as the largest essential extension of V, thus can be regarded as the Hilbert C*-module version of the multiplier algebra. The extended module Vd of the generalized Hilbert space over A is explicitly determined as a Hilbert C*-module of sequences in M(A) containing the generalized Hilbert space over M(A).
