Year: 2026
Type: preprint
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 $Ψ=\{ψ_k\}_{k=1}^{\infty}$ and a matrix $E$ under which $EΨ$ 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.
Source: arXiv (Cornell University)
Authors: Rad, Hassan Hedayati, Shateri, Tayebe Lal
Institution: Hakim Sabzevari University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204917862