线性算子在商空间上的诱导算子的若干性质

Some Properties of Deduced Operator on Quotient Space by a Linear Operator

论证了线性算子f在模f的核的商空间上所诱导的算子保持f的有界性及闭性,Banach空间上满的线性算子f所诱导的算子T:X/X0→X/f(X0)保持f的紧性,并且当f为线性同构时,T是线性同胚映射。

In this paper, it is proved that the operator deduced on the quotient space moduled by the kernel of a linear operator f preserves the boundedness and closedness of f, and that the operator T： X/X0→X/f（X0） deduced by a surjective linear operator f on a Banach space preserves the compactness of f and T is homeomorphic if f is isomorphic.