Extensions of Hilbert C*-modules

• Autores: Boris Guljas, Damir Bakic
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 30, Nº 2, 2004, págs. 537-558
• Idioma: inglés
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• Resumen

  • 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).