有界齐性算子空间及其应用

本文证明了赋范线性空间中有界齐性算子与在零点连续的齐性算子等价,对两个赋范线性空间X与Y之间的有界齐性算子全体H（X,Y）,按引入的范数及线性运算,构成赋范线性空间;证明了有界齐性算子空间H（X,Y）为Banach空间当且仅当空间Y是完备的,最后,我们给出有界齐性算子空间在算子广义逆问题上的应用。

THE SPACE OF BOUNDED HOMOGENEOUS OPERATORS AND ITS APPLICATION

In this paper, the equivalent relation of boundedness and continuity at zero for homogeneous operator in normal linear space is proved. let X and Y be normal linear space, and H(X,Y) the set of all bounded homogeneous operators between X and Y . According to the morm and linear operation introduced, we prove that H(X,Y) is normal linear space. H(X,Y) is complete if and only if the space Y is Banach space. Finally, the application of bounded homogeneous operator space to generalized inverses of operator are given in this paper as well.