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

In this paper, we demonstrate notion of -morphism ofhilbert h-modules and describe some properties of these module maps.moreover, we show that if  : a ! b is an injective morphism of simpleh-algebras, the range of |(a) is b-closed, {ei}i2i is a maximalfamily of doubly orthogonal minimal projections for a, : e ! f is asurjective -morphism of hilbert h-modules, {u,i}2 is an orthonormalbasis for e in which for each  2 , [u,i|u,i] = ei (i 2 i) andf is full, then {(ei)}i2i and {(u,i)}2 are maximal family of doublyorthogonal minimal projections for b and orthonormal basis for frespectively.