AI 中文总结
本文系统研究了Banach空间中的g-对偶Banach框架，建立了其存在条件，探讨了与其他广义对偶概念的关系，并证明了其在有界扰动下的稳定性。
AI 中文摘要
本文在Banach空间X及其对偶空间X?中，给出了g-对偶Banach框架的全面表述和系统研究。我们研究了这些框架的基本结构性质，并建立了其存在的充分条件。此外，我们探讨了它们与Banach框架理论中其他广义对偶概念的关系。最后，我们研究了g-对偶Banach框架在有界扰动下的稳定性，证明了其在泛函分析中的鲁棒性和潜在应用。
英文摘要
This paper presents a comprehensive formulation and a systematic investigation of g-dual Banach frames in a Banach space X and its dual space X?. We study the fundamental structural properties of these frames and establish sufficient conditions for their existence. Furthermore, we explore their relationships with other generalized notions of duality in Banach frame theory. Finally, we investigate the stability of g- dual Banach frames under bounded perturbations, demonstrating their robustness and potential applications in functional analysis.
Comments36 pages
