论文标题
Hilbert太空运营商的GD1逆和1GD逆
GD1 inverse and 1GD inverse for Hilbert space operators
论文作者
论文摘要
Mosic和Djordjevic在[J.频谱。理论，8（2）：555-573，2018]，考虑与摩尔 - 柔性倒数逆的普遍性Drazin。本文介绍了两种新的倒置类别：Hilbert空间运营商的GD1（广义Drazin和内部）倒数和1GD（内部和广义Drazin）逆。讨论了GD1（也是1GD）逆的存在和唯一性，以及通过核心质量分解和封闭范围分解算子的某些属性。我们进一步建立了GD1逆的一些明确表示及其与广义Drazin逆的互连。此外，我们通过二进制关系讨论了GD1（也是1GD）逆的一些属性。
Mosic and Djordjevic introduced the notation of the gDMP inverse for Hilbert space operators in [J. Spectr. Theory, 8(2):555-573, 2018] by considering generalized Drazin inverse with the Moore-Penrose inverse. This paper introduces two new classes of inverses: GD1 (generalized Drazin and inner) inverse and 1GD (inner and generalized Drazin) inverse for Hilbert space operators. The existence and uniqueness of the GD1 (also 1GD) inverse are discussed, along with some properties through core-quasinilpotent decomposition and closed range decomposition operator. We further establish a few explicit representations of the GD1 inverse and their interconnections with generalized Drazin inverse. In addition, we discuss a few properties of GD1 (also 1GD) inverse through binary relation.
