发表机构
Department of Mathematics, University of Delhi（德里大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为可分Hilbert空间中Hilbert-Schmidt框架的扰动稳定性建立了基于Nagy型和Pollard-Hilding型不等式的充分条件，并提供了框架界的显式估计及示例。
AI 中文摘要
我们建立了若干充分条件，确保可分Hilbert空间中给定Hilbert-Schmidt框架的扰动算子族仍为Hilbert-Schmidt框架。这些扰动准则通过Nagy型和Pollard-Hilding型不等式表述，并给出了所得框架界的显式估计。文中给出了几个例子以说明结果的适用性。
英文摘要
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.
