线性空间上的线性算子的自反性

Reflexivity of Linear Operators on a Linear Space

论证了Banach空间X上的有界线性算子B是2-自反的。2-自反不一定意味着自反,但是,如果X是复数域上的无限维的线性空间,B是X上的线性变换,而且WB={p(B):p是任意的复数系数的多项式}是严格循环的,则B是代数性自反的。

This paper proved that a bounded linear operator on a Banach space is 2-reflexive. But 2-reflexivity doesn't imply reflexivity. However, if X is an infinite dimentional linear space and WB={p(B)}:p∈F[t],a polynomial with complex coefficients} is strictly cyclic, then is algebraically reflexive.