φ-positively full Hilbert C* -modules and an application

Let A and B be C -algebras, φ : A ! B be a linear * -homomorphism, and let Mand N be Hilbertmodules over C* -algebras A and B, respectively. In this talk, we state the de nition of morphisms betweenHilbert modules and demonstrate the notion of '-positively full Hilbert modules. In particular, we showthat for a *-monomorphism φ : A → B and a surjective φ-morphism T : M → N if N is φ-positivelyfull, then M is φ-۱-positively full. Finally, introducing the concepts of the implemented Hilbert moduleand unitary equivalence, we show that the Hilbert B-module N and the implemented Hilbert A-moduleM(φ;T ) are unitary equivalent.

کلیدواژه ها:

Full Hilbert C* -module ، unitary operator