算子的对偶特征与开映射定理

DUAL CHARATERS OF OPERATORS AND OPEN MAPPING THEOREM

先给出了局部凸空间上线性算子的各种闭性和各种连续性的对偶特征.然后利用算子T与(?)的关系,从连续性的对偶特征得到了相对开映射的对偶特征,推广了Grothendieck的拓扑同态定理.最后用同样的办法,从闭图象定理得到了Ptak开映射定理的一个推广.

In this paper, we first give the dual characters of some kinds of closeness and continuity for linear operators on locally convex spaces. Then we obtain the dual characters of relatively open mappings from thedual characters of continuous mappings with the relations between the operator T and T, which extends theGrothendieck's topological homorphism theorem. At last, we obtain a extenaion of Ptak's open mapping theorem from the closed graph theorem with the same method.