On frames in Hilbert modules over pro-C*-algebras

TL;DR

This paper introduces the concept of frames of multipliers in Hilbert modules over pro-C*-algebras, extending properties known from Hilbert C*-modules to this broader setting.

Contribution

It defines frames of multipliers in Hilbert modules over pro-C*-algebras and demonstrates that many properties from Hilbert C*-modules carry over.

Findings

Frames of multipliers are well-defined in Hilbert modules over pro-C*-algebras.

Many properties of frames in Hilbert C*-modules are valid for these new frames.

The work broadens the understanding of frame theory in the context of pro-C*-algebras.

Abstract

We introduce the concept of frame of multipliers in Hilbert modules over pro-C*-algebras and show that many properties of frames in Hilbert C*-modules are valid for frames of multipliers in Hilbert modules over pro-C*-algebras.