On multipliers of Hilbert modules over locally C*-algebras

TL;DR

This paper explores the structure of multiplier modules over locally C*-algebras and examines the relationship between adjointable operators on original modules and their multiplier modules.

Contribution

It provides new insights into the structure of multiplier modules and the connection between adjointable operators on modules and their multipliers over locally C*-algebras.

Findings

Characterization of multiplier modules over locally C*-algebras

Relationship between adjointable operators on modules and their multipliers

Structural properties of Hilbert modules in this context

Abstract

In this paper, we investigate the structure of the multiplier module of a Hilbert module over a locally C*-algebra and the relationship between the set of all adjointable operators from a Hilbert A-module E to a Hilbert A-module F and the set of all adjointable operators from the multiplier module M(E)of E to the multiplier module M(F) of F.