J-Frame Sequences in Krein Space

Abstract

Let $\{f_n:n\in \mathbb{N}\}$ be a $J$-frame for a Krein space $\text{K}$ and $P_M$ be a $J$-orthogonal projection from $\text{K}$ onto a subspace $M$. In this article we find sufficient conditions under which $\{P_M(f_n):n\in \mathbb{N}\}$ is a $J$-frame for $P_M\text{K}$ and $\{(I-P_M)f_n{\}}_{n\in \mathbb{N}}$ is a $J$-frame for $(I-P_M)\text{K}$. We also introduce $J$-frame sequence for a Krein space $\text{K}$ and study some properties of $J$-frame sequence analogues to Hilbert space frame theory.