A Note on -Morphisms of Hilbert H-Modules

Abstract

In this paper, we demonstrate notion of -morphism of Hilbert H-modules and describe some properties of these module maps. Moreover, we show that if : A ! B is an injective morphism of simple H-algebras, the range of | (A) is B-closed, {ei}i2I is a maximal family of doubly orthogonal minimal projections for A,  : E ! F is a surjective -morphism of Hilbert H-modules, {u,i}2 is an orthonormal basis for E in which for each  2 , [u,i|u,i] = ei (i 2 I) and F is full, then { (ei)}i2I and {(u,i)}2 are maximal family of doubly orthogonal minimal projections for B and orthonormal basis for F respectively.