J-Frame Sequences in Krein Space

Abstract: Let ${f_n:n\in\mathbb{N}}$ be a $J$-frame for a Krein space ${\textbf{\textit{K}}}$ and $P_M$ be a $J$-orthogonal projection from ${\textbf{\textit{K}}}$ 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 $P_M\textbf{\textit{K}}$ and ${(I-P_M)f_n}_{n\in{\mathbb{N}}}$ is a $J$-frame for $(I-P_M)\textbf{\textit{K}}$. We also introduce $J$-frame sequence for a Krein space ${\textbf{\textit{K}}}$ and study some properties of $J$-frame sequence analogues to Hilbert space frame theory.