Frames in Krein spaces arising from a non-regular W-metric

TL;DR

This paper extends the concept of frames to Krein spaces, providing a complete characterization and methods to transfer frames from Hilbert spaces to Krein spaces with non-regular, possibly unbounded W-metrics.

Contribution

It introduces a new framework for frames in Krein spaces and characterizes them via comparison with Hilbert space frames, including non-regular and unbounded W-metrics.

Findings

Complete characterization of frames in Krein spaces.

Method to transfer Hilbert space frames to Krein spaces with non-regular W-metric.

Framework accommodating unbounded Gram operators.

Abstract

A definition of frames in Krein spaces is stated and a complete characterization is given by comparing them to frames in the associated Hilbert space. The basic tools of frame theory are described in the formalism of Krein spaces. It is shown how to transfer a frame for Hilbert spaces to Krein spaces given by a W-metric, where the Gram operator W is not necessarily regular and possibly unbounded.