H-Operator Approximation Spaces via Delayed Riesz Means and Quasi-Banach Moduli
Abstract
We establish a constructive and quasi-Banach framework for approximation spaces Aμρ of compact H-operators between Banach and quasi-Banach spaces. By leveraging delayed Riesz means V2bn generated by self-adjoint differential operators P(D), we replace abstract best approximants with explicit linear operator decompositions. Furthermore, we extend the theory of H-operator approximation spaces to quasi-Banach settings (0 < p < 1), bypassing the collapse of Peetre's K-functional by employing localized moduli of smoothness ωφr(f,t)p. Integrating seminal spectral bounds due to Markus \cite{M1966} and factorization techniques for operator ideals, we prove that operators belonging to Aμρ possess complete systems of root vectors whose expansions are Abel summable.
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BibTeX
@misc{thiong2026hoperator,
title = {{$H$-Operator Approximation Spaces via Delayed Riesz Means and Quasi-Banach Moduli}},
author = {Daniel Akech Thiong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14381},
eprint = {2609.14381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14381},
}
RIS
TY - UNPB
TI - H-Operator Approximation Spaces via Delayed Riesz Means and Quasi-Banach Moduli
AU - Daniel Akech Thiong
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14381
UR - https://arxiv.org/abs/2609.14381
AB - We establish a constructive and quasi-Banach framework for approximation spaces A_μ^ρ of compact H-operators between Banach and quasi-Banach spaces. By leveraging delayed Riesz means V_2^bn generated by self-adjoint differential operators P(D), we replace abstract best approximants with explicit linear operator decompositions. Furthermore, we extend the theory of H-operator approximation spaces to quasi-Banach settings (0 < p < 1), bypassing the collapse of Peetre's K-functional by employing localized moduli of smoothness ω_φ^r(f,t)_p. Integrating seminal spectral bounds due to Markus \cite{M1966} and factorization techniques for operator ideals, we prove that operators belonging to A_μ^ρ possess complete systems of root vectors whose expansions are Abel summable.
ER -