关于Banach共轭算子和Hilbert共轭算子的讨论

Discussion on Banach conjugate operator and Hilbert conjugate operator

Banach共轭算子和Hilbert共轭算子是泛函分析中两个非常重要的概念.Hilbert空间是特殊的Banach空间,但Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子的定义,并且绝大数教材都没有说明这样定义的原因.阐述了Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子定义的原因,并讨论Hilbert空间中这两种算子的关系.

Banach conjugate operator and Hilbert conjugate operator are two very important concepts in functional analysis. Hilbert space is a special Banach space,but the conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and thevast majority textbooks don′t explain the reasons for this definition.Described the reason why conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and discussed the relationship between the two operators.