集值映射的连续选择与线性算子的齐性右逆

本文对于取值在Ｂａｎａｃｈ空间的几乎下半连续映射引入两个相关的下半连续闭凸集值映射，得到集值映射的连续选择存在性的若干特征，从而将 Ｄｅｕｔｓｃｈ Ｅ，和Ｋｅｎｄｅｒｏｖ Ｐ，Ｄｅ Ｂｌａｓｔ Ｆ．Ｓ．和 Ｍｙｊａｋ Ｊ，Ｐｒｚｅｓｌａｗｓｋｉ Ｋ．和 Ｒｙｂｉｎｓｋｉ Ｌ Ｅ，Ｇｕｔｅｖ Ｖ．等人以及作者自己的关于连续选择存在性的结果作为推论给出．并用这些结论讨论了在开映射定理不成立的。情况下从Ｂａｎａｃｈ空间到赋范空间上线性连续算子的齐性右逆存在问题．

Continuous Selections Set-Valued Mapping and Homogeneous Right Inverses of Linear Operators

In this paper, we introduce two lower semicontinuous closed convex set-valued mappings relating to almost lower semicontinous set-valued mappings in Banach spaces, give several characteristics on the existence of continuous selections for set-valued mappings. As the corollaries, the results of Deutsch and Kenderov, De Blasi and Myjak, Przeslawski and Rybinski, Gutev and author about the existence of continuous selections are obtained again. On the basis this, we discuss the problem about the existence of homogenoous right inverses for linear operators from Banach space into normed spaces when the open mapping theorem does not hold.