Banach空间中线性算子的Tseng度量广义逆

THE TSENG-METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SACES

在 Ｂａｎａｃｈ空间中，利用 Ｂａｎａｃｈ几何方法及度量投影算子，将 Ｅ．Ｈ．Ｍｏｏｒｓ的学生，曾远荣（Ｙ．Ｙ． Ｔｓｅｎｇ）在 Ｈｉｌｂｅｒｔ空间中为线性算子引入的 Ｔｓｅｎｇ广义道，推广到 Ｂａｎａｃｈ空间，引入 Ｔｓｅｎｇ度量广义逆（此时的 Ｔｓｅｎｇ度量广义逆一般为齐性算子，而非线性算子），利用 Ｂａｎａｃｈ空间对偶映射与广义正交分解定理给出 Ｔｓｅｎｇ度量广义道存在的充分必要条件．讨论了最大Ｔｓｅｎｇ度量广义逆在最优化，控制论及微分方程不适定问题有着直接应用的一些基础性质．

The concept of Tseng-metric generalized inverse of linear operator in Banach spaces is introduced in this papert by Tseng Y.Y, a student of E.H. Moors, for Hilbert spaces generalizing that defined. Unlike the case in Hilbert spaces, the Tseng-metric generalized inverse of linear operator in Banach space is usually homogeneous, and nonlinear. By means of the dual mapping and geometric properties of Banach spaces, the necessary and sufficient condition for existence of the Tseng metric generalized inverse is given, and the properties of the maximum Tseng metric generalized inverse is disscused in this paper as well.