Hilbert modules and their representation

Abstract

A Hilbert module over a C*-algebra A with identity is an unitary A-module H, endowed with an inner product taking values in A. We consider these modules and derive some of their elementary properties. Later we consider fields of Hilbert modules and obtain a representation of H by means of continuous sections. This result will be used in other papers ([7] and [8]) to get a duality theorem and to study special Hilbert modules.