Properties of $J$-fusion frames in Krein spaces

Abstract

In this article we introduce the notion of $J$-Parseval fusion frames in a Krein space $\mathbb{K}$ and characterize 1-uniform $J$-Parseval fusion frames with $\zeta=\sqrt{2}$. We provide some results regarding construction of new $J$-tight fusion frame from given $J$-tight fusion frames. We also characterize an uniformly $J$-definite subspace of a Krein space $\mathbb{K}$ in terms of $J$-fusion frame. Finally we generalize the fundamental identity of Hilbert space frames in the setting of Krein spaces.