A Note on Phi-Morphisms of Hilbert H*-Modules

Abstract

In this paper, we demonstrate notion of -morphism of Hilbert H-modulesand describe some properties of these module maps. Moreover, we show that if : A ! Bis an injective morphism of simple H-algebras, the range of j(A) is B-closed, feigi2I is amaximal family of doubly orthogonal minimal projections for A, : E ! F is a surjective-morphism of Hilbert H-modules, fu;ig2 is an orthonormal basis with supportingprojection ei (i 2 I) for E and F is full, then f(ei)gi2I and f(u;i)g2 are maximal familyof doubly orthogonal minimal projections for B and orthonormal basis for F respectively.