$H$-算子逼近空间：通过延迟Riesz均值和拟Banach模
$H$-Operator Approximation Spaces via Delayed Riesz Means and Quasi-Banach Moduli
- Claremont Graduate University（克莱蒙特研究生大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文为紧$H$-算子建立拟Banach逼近空间框架，用延迟Riesz均值构造显式分解，并扩展至$0<p<1$情形，证明根向量系展开的Abel可和性。
AI中文摘要：
我们为Banach和拟Banach空间之间的紧$H$-算子建立了构造性的拟Banach框架，用于逼近空间$A_\mu^\rho$。通过利用由自伴微分算子$P(D)$生成的延迟Riesz均值$V_{2^{bn}}$，我们用显式线性算子分解替代了抽象最佳逼近元。此外，我们将$H$-算子逼近空间理论扩展到拟Banach设置（$0 < p < 1$），通过采用局部光滑模$\omega_\varphi^r(f,t)_p$绕过了Peetre的$K$-泛函的退化。结合Markus \cite{M1966}的谱界和算子理想分解技术，我们证明了属于$A_\mu^\rho$的算子具有完整的根向量系，其展开是Abel可和的。
英文摘要：
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.
