# J-fusion frame operator for Krein spaces

## TL;DR

This paper characterizes $J$-fusion frames in Krein spaces, provides bounds approximation, and explores conditions for operators preserving $J$-fusion frame structure, advancing the understanding of frame theory in indefinite inner product spaces.

## Contribution

It establishes necessary and sufficient conditions for $J$-fusion frames, approximates frame bounds, and characterizes operators that preserve $J$-fusion frames in Krein spaces.

## Key findings

- Characterization of $J$-fusion frames in Krein spaces.
- Approximation of $J$-fusion frame bounds.
- Conditions for operators preserving $J$-fusion frames.

## Abstract

In this article we find a necessary and sufficient condition under which a given collection of subspace is a $J$-fusion frame for a Krein space $\mathbb{K}$. We also approximate $J$-fusion frame bounds of a $J$-fusion frame by the upper and lower bounds of the synthesis operator. Then, we obtain the $J$-fusion frame bounds of the cannonical $J$-dual fusion frame. 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.