广义正交分解定理与Tseng度量广义逆

本文将Banach空间中广义正交分解定理从线性子空间拓广至非线性集—太阳集,分别给出了一算子为度量投影算子和一度量投影算子为有界线性算子的充要条件;得到了判别Banach空间中子空间广义正交可补的充要条件;建立了王玉文和季大琴(2000年)新近引入的Banach空间中的线性算子的Tseng度量广义逆存在的特征刻划条件;这些工作本质地把王玉文等人的新近结果从自反空间拓广至非自反空间的情形.

GENERALIZED ORTHOGONAL DECOMPOSITION THEOREM AND THE TSENG-METRIC GRNERALIZED INVERSE

In this paper, a generalized orthogonal decomposition theorem in Banach space is extended from linear subspace to nonlinear subset-sun set, and the conditions which are sufficient and necessary for an operator to be a metric projection operator and a metric projection operator to be a bounded linear operator are given. Characterization condition for a subspace in Banach space to be generalized orthogonal complemented is obtained. The necessary and sufficient condition for existence of the Tseng-metric generalized inverse of linear operator in Banach spaces introduced recently by Wang Yuwen and Ji Daqin (2000) is established. These results indeed extend and improve the corresponding work done by Wang Yuwen and others from reflexive Banach space to non-reflexive Banach space recently.