J-fusion frame for Krein spaces

TL;DR

This paper introduces the concept of J-fusion frames in Krein spaces, relating them to existing frames in Hilbert and Krein spaces, and explores their properties, bounds, and operator characterizations.

Contribution

It defines J-fusion frames for Krein spaces, connects them with existing frame concepts, and investigates their bounds and operator invariance.

Findings

J-fusion frames are related to fusion frames in Hilbert spaces.

Bounds of J-fusion frames can be approximated via synthesis operator bounds.

Characterization of operators preserving J-fusion frames is provided.

Abstract

In this article we introduce the notion of $J$-fusion frame for a Krein space $\mathbb{K}$. We relate this new concept with fusion frames for Hilbert spaces and also with $J$-frames for Krein spaces. We also approximate $J$-fusion frame bounds of a $J$-fusion frame by the upper and lower bounds of the synthesis operator. Finally we address the problem of characterizing those bounded linear operators in $\mathbb{K}$ for which the image of $J$-fusion frame is also a $J$-fusion frame.