E-K-FRAMES IN HILBERT SPACES
Keywords:
Infinite matrix, E-K-frame, E-atomic systemAbstract
In this paper, we introduce $E$-$K$-frames for a separable Hilbert space $\mathcal{H}$, where $E$ is an infinite matrix of real or
complex numbers, and $K$ is a bounded operator on $\mathcal{H}$. Actually, $E$-$K$-frames are a kind of generalization of $K$ frames by infinite matrices.
Assuming an (invertible) infinite matrix $E$ as a mapping on the Hilbert space $\bigoplus _{n=1}^{\infty}\mathcal{H}_n$, we
aim to study the properties of $E$-$K$-frames, define the notion of $E$-atomic system for an operator $K$ on $\mathcal{H}$ and address its relationship by $E$-$K$-frames.
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