PreprintCC BY 4.0arXiv
Nagy and Pollard-Hilding-Type Stability of Hilbert-Schmidt Frames
Abstract
We establish several sufficient conditions ensuring that a perturbed family of operators in a given Hilbert-Schmidt frame for a separable Hilbert space remains a Hilbert-Schmidt frame. The perturbation criteria are formulated through Nagy-type and Pollard-Hilding-type inequalities, yielding explicit estimates for the resulting frame bounds. Several examples are presented to illustrate the applicability of the results.
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BibTeX
@misc{jyoti2026nagy,
title = {{Nagy and Pollard-Hilding-Type Stability of Hilbert-Schmidt Frames}},
author = {Jyoti and Ruchi and Lalit Kumar Vashisht},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22528},
eprint = {2609.22528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22528},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nagy and Pollard-Hilding-Type Stability of Hilbert-Schmidt Frames
AU - Jyoti
AU - Ruchi
AU - Lalit Kumar Vashisht
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22528
UR - https://arxiv.org/abs/2609.22528
AB - We establish several sufficient conditions ensuring that a perturbed family of operators in a given Hilbert-Schmidt frame for a separable Hilbert space remains a Hilbert-Schmidt frame. The perturbation criteria are formulated through Nagy-type and Pollard-Hilding-type inequalities, yielding explicit estimates for the resulting frame bounds. Several examples are presented to illustrate the applicability of the results.
ER -