Study of weaving frames in Krein spaces

TL;DR

This paper explores the properties and applications of weaving frames in Krein spaces, extending frame theory to indefinite inner product spaces and demonstrating their use in probabilistic erasure scenarios.

Contribution

It provides new characterizations of Krein space weaving frames and discusses their application in data loss mitigation, expanding the theoretical framework and practical relevance.

Findings

Characterization of Krein space weaving frames

Examples and counterexamples illustrating theoretical results

Application to probabilistic erasure scenarios

Abstract

Inspired by the work of Bemrose et al. \cite{Be16}, we delve into the study of weaving frames in Krein spaces. This paper presents a comprehensive exploration of various properties and characterizations of Krein space weaving frames. In support of our findings, several examples and counter examples are provided, illustrating the applicability of the theoretical results. Additionally, we extend the discussion to an important application in probabilistic erasure, highlighting how weaving frames can be used to mitigate data loss in such scenarios. This work contributes to the broader understanding of frame theory in indefinite inner product spaces.