Moore-Penrose广义逆和最佳逼近算子的表达式

Moore-Penrose Generalized Inverse and the Representive of Best Approximation Operator

在空间较弱的几何假定下,给出了 A+ 的存在唯一性、极小性,并建立了 A+ 为线性算子的充 要条件。还给出了一般 Banach 空间中线性流形上的最佳逼近算子存在的充要条件,并借助于正 规对偶映射得到了相应的最佳逼近算子的表达式。所得的结果推广和改进了他人的相应结果。

Under the weaker geometry assumption of spaces, the existence-uniqueness and minimum property of A+ is given, and the necessary and su?cient condition for operator A+ to be linear is established. Meanwhile we give the necessary and su?cient condition for existence of best approx- imation operator on the linear manifold in arbitary Banach space, and obtain a representive of the corresponding best approximation operator by the normalized duality mapping. These generalize and improve the recent corresponding results obtained by others.