集值度量广义逆的定义域

THE DEFINITIONAL DOMAIN OF SET-VALUED METRIC GENERALIZED INVERSE

设X、Y为Banach空间,T∈L(X,Y)为线性算子,T的核N(T)为迫近集,T的值域R(T)在Y中为逼近紧的.本文征得T的度量广义逆T的定义域D(T)=Y,由此不适定线性算子方程Tx=y,对任意y∈Y均有最佳逼近解.

Amuse X, Y is Banach space, T ∈ L（X, Y） is liner operator N（T） is approximate set and R（T） is approximate compact in Y, this paper proves D（ T^δ） = Ywhere T^δ is metric generalized inverse of T, Hence arbitrary y ∈Y, illposed liner operator equation Tx = y exists the best aooroximate solution