关于紧算子的若干探讨

Notes on Compact Operators

给出严格奇异空间及严格余奇异空间上算子T是紧的充分必要条件,证明了对任意复无限维的Hilbert空间H,有K(H)=I(H)成立,并给出对于Banach空间X,使K(X)=I(X)不成立的一个反例。

Gives the necessary and sufficient condition for T is compact operator on strictly singular spaces or strictly cosingular spaces,proves that K（H）=I（H）for any Hilbert space H,and gives a counter-example on Banach space X where K（X）=I（X）does not hold.