Without geometry assumption on strictly convex space,by means of methods of geometry of Banach space,the necessary and sufficient conditions for the existence, uniqueness,minimum property and linearity of the Moore-Penrose metric generalized inverse T~+ of linear operator T are given,and some properties of T~+ are investigated. These indeed extend and improve the corresponding recent results obtained by [8] from strictly convex Banach space to arbitrary Banach space.
Ren Xing NI.
Moore-Penrose Metric Generalized Inverse of Linear Opeartor in Arbitrary Banach Space. Acta Mathematica Sinica, Chinese Series, 2006, 49(6): 1247-125 https://doi.org/10.12386/A2006sxxb0156