发表机构
School of Big Data, Fuzhou University of International Studies and Trade（福州外语外贸大学大数据学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Banach *-代数中提出广义加权核逆，通过广义加权核分解和加权g-Drazin逆刻画其性质，并推广至复矩阵，统一了core-EP逆与广义核逆。
AI 中文摘要
我们在Banach *-代数中引入了关于两个元素的广义加权核逆，扩展了现有广义逆的框架。这一新的广义逆通过广义加权核分解来刻画，并利用加权g-Drazin逆建立了其表示。我们研究了极类似性质和主理想性质以揭示其结构行为。由此，推导出了对复矩阵的应用。这涵盖了core-EP逆和广义核逆，显著拓宽了理论框架。
英文摘要
We introduce the generalized weighted core inverse with respect to two elements in a Banach *-algebra, extending the framework of existing generalized inverses. This new generalized inverse is characterized via the generalized weighted core decomposition, and its representations are established using the weighted g-Drazin inverse. We investigate the polar-like and principal ideal properties to reveal its structural behavior. Consequently, applications to complex matrices are derived. This finds encompasses both the core-EP and generalized core inverses, significantly broadening the theoretical framework.
