AI 中文总结
研究在 * - 巴拿赫代数框架内广义 (b,c) EP 逆的概念，通过相关分解、广义 Drazin 逆等给出其特征刻画，呈现极型性质，揭示其与广义群逆反序律联系。
AI 中文摘要
本文在 * - 巴拿赫代数框架内引入广义 (b,c) EP 逆的概念。此概念是弱群逆和类 EP 性质的逻辑扩展，适用于复矩阵和希尔伯特空间中的有界线性算子。给出其与相关分解及广义 Drazin 逆的特征刻画，呈现广义 (b,c) EP 逆的极型性质，还揭示广义 (b,b) EP 逆与广义群逆反序律的内在联系。
英文摘要
In this paper, we introduce the notion of the generalized (b,c) EP inverse within the framework of a *-Banach algebra. This concept emerges as a logical extension of the weak group inverse and EP-like property, which is applicable to complex matrices and bounded linear operators in Hilbert spaces. We provide its characterizations in relation to its associated decomposition and the generalized Drazin inverse. A polar-like property for the generalized (b,c) EP inverse is presented. Furthermore, we reveal an intrinsic connection between the generalized (b,b) EP inverse and the converse law for the generalized group inverse.
