On quasi-free Hilbert modules

TL;DR

This paper addresses technical questions about finite rank quasi-free Hilbert modules, offering methods to determine unitary equivalence, representations for module maps, and insights into their holomorphic structures.

Contribution

It develops new techniques for analyzing finite rank quasi-free Hilbert modules, including criteria for unitary equivalence and representations of module maps.

Findings

Provided a method to determine unitary equivalence of modules

Developed representations for module maps

Studied the holomorphic structure on quasi-free Hilbert modules

Abstract

In this note we settle some technical questions concerning finite rank quasi-free Hilbert modules and develop some useful machinery. In particular, we provide a method for determining when two such modules are unitarily equivalent. Along the way we obtain representations for module maps and study how to determine the underlying holomorphic structure on such modules.