$E$-$g$-frames

Abstract

In the present paper, we introduce the notion of $E$-$g$-frames for a separable Hilbert spaces $\mathcal{H}$, where $E$ is an invertible infinite matrix mapping on the Hilbert space $\underset{n=1}{\overset{\infty }{\oplus }}{\mathcal{H}}_n$. We study some prperties of $E$-$g$-frames. First, we give a result concerning perturbation of $E$-$g$-frames and then use it to construct $E$-$g$-frames in separable Hilbert spaces.