本性不可比的Banach空间

On Essentially Incomparable Banach Spaces

通过引入本性严格奇异算子和投影严格奇异算子 ,讨论本性不可比的 Banach空间 ,对 M.Gonzalez提出的猜想作出部分的肯定回答 .最后 ,利用空间的本性不可比构造了一类空间 。

In this paper, we introduce essentially strictly singular operators and projectionally strictly singular operators, discuss essentionally incomparable Banach spaces and give a partial answer to the conjecture of M.Gonzalez. Finally, we construct a class of Banach spaces on which the class of inessential operators does not coincide with the class of strictly cosingular operators by using essential incomparability of Banach spaces.