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arXiv · 2608.30592

Infinite Matrix Operators and $E$-Frames in Hilbert Spaces

Hassan Hedayati Rad·Tayebe Lal Shateri
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Abstract

The concept of an $E$-frame, recently introduced in frame theory, is obtained by applying an infinite invertible complex matrix to a sequence of elements of a Hilbert space $\mathcal{H}$. Here, $E$ is considered as a matrix mapping on the sequence space $\bigoplus_{n=1}^{\infty}\mathcal{H}$. A natural question is to determine the conditions on a sequence $\Psi=\{\psi_k\}_{k=1}^{\infty}$ and a matrix $E$ under which $E\Psi$ becomes a frame. In this paper, we show that if $E$ acts surjectively on $\bigoplus_{n=1}^{\infty}\mathcal{H}$, then every ordinary frame is an $E$-frame.

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BibTeXRIS

Hassan Hedayati Rad, Tayebe Lal Shateri. 2026-08-31. Infinite Matrix Operators and $E$-Frames in Hilbert Spaces. https://arxiv.org/abs/2608.30592

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