两个可补子空间和的可补性  

The Complementarity of the Sum of Two Complemented Subspaces

作　　者：吴祝宁[1] 

机构地区：[1]华侨大学管理信息科学系

出　　处：《华侨大学学报（自然科学版）》1999年第1期15-17,共3页Journal of Huaqiao University(Natural Science)

摘　　要：指出Ｂａｎａｃｈ空间Ｘ的两个可补子空间之和未必再是Ｘ的可补子空间，但当Ｐ和Ｑ都是Ｘ上连续线性投影算子且ＰＱ是严格奇异算子时，ＰＸ＋ＱＸ是可补的．进而推出有限个两两不可比的可补子空间之和是可补的．As pointed by the author, the sum of two complemented subspaces of Banach space X may not be complemented space of X ; however, when P and Q are all continuous linear projection operators on X and PQ are strictly singular operators, PX+QX are complemented. As further inferred by the author, the sum of pairwisely incomparable and complemented subspaces limited in number is complemented.

关 键 词：可补子空间 投影算子 和 巴拿赫空间 可补性 

分 类 号：O177.2[理学—数学]