Hilbert modules over locally C*-algebras

TL;DR

This paper explores Hilbert modules over locally C*-algebras, proving that their adjointable endomorphisms form a locally C*-algebra, thus extending the understanding of module structures in this context.

Contribution

It provides a detailed proof that the set of adjointable endomorphisms of Hilbert modules over locally C*-algebras is itself a locally C*-algebra, clarifying foundational properties.

Findings

The set of adjointable endomorphisms forms a locally C*-algebra.

Detailed proof of the main structural result.

Enhanced understanding of Hilbert modules over locally C*-algebras.

Abstract

In the present paper the notion of a Hilbert module over a locally C*-algebra is discussed and some results are obtained on this matter. In particular, we give a detailed proof of the known result that the set of adjointable endomorphisms of such modules is itself a locally C*-algebra.