PreprintCC BY 4.0arXiv
Normalized Orbit Frames and Essential Spectrum, II
Abstract
Given 0<rj<1 with rj→1, there exist a normal operator T on ℓ2 with eigenvalues λj satisfying |λj|=rj and g∈ℓ2 such that { Tng/(‖ Tng‖ )} n≥0is a frame Longleftrightarrow ∑j≥1(1−r2j)=∞. Whenever this condition holds, the frame bounds can be chosen with ratio arbitrarily close to one.
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BibTeX
@misc{tian2026normalized,
title = {{Normalized Orbit Frames and Essential Spectrum, II}},
author = {James Tian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19545},
eprint = {2610.19545},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19545},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Normalized Orbit Frames and Essential Spectrum, II
AU - James Tian
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19545
UR - https://arxiv.org/abs/2610.19545
AB - Given 0<r_j<1 with r_j→1, there exist a normal operator T on ℓ^2 with eigenvalues λ_j satisfying |λ_j|=r_j and g∈ℓ^2 such that { T^ng/(‖ T^ng‖ )} _n≥0is a frame Longleftrightarrow ∑_j≥1(1−r^2_j)=∞. Whenever this condition holds, the frame bounds can be chosen with ratio arbitrarily close to one.
ER -