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Infinite Matrix Operators and E-Frames in Hilbert Spaces
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 ℋ. Here, E is considered as a matrix mapping on the sequence space ⨁n=1∞ℋ. A natural question is to determine the conditions on a sequence Ψ={ψk}k=1∞ and a matrix E under which EΨ becomes a frame. In this paper, we show that if E acts surjectively on ⨁n=1∞ℋ, then every ordinary frame is an E-frame.
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BibTeX
@misc{rad2026infinite,
title = {{Infinite Matrix Operators and $E$-Frames in Hilbert Spaces}},
author = {Hassan Hedayati Rad and Tayebe Lal Shateri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.30592},
eprint = {2608.30592},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30592},
}
RIS
TY - UNPB
TI - Infinite Matrix Operators and E-Frames in Hilbert Spaces
AU - Hassan Hedayati Rad
AU - Tayebe Lal Shateri
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2608.30592
UR - https://arxiv.org/abs/2608.30592
AB - 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 ℋ. Here, E is considered as a matrix mapping on the sequence space ⨁_n=1^∞ℋ. A natural question is to determine the conditions on a sequence Ψ={ψ_k}_k=1^∞ and a matrix E under which EΨ becomes a frame. In this paper, we show that if E acts surjectively on ⨁_n=1^∞ℋ, then every ordinary frame is an E-frame.
ER -