Prespectral operators

Abstract

is called pre-imaging function for x and T. It is easily shown that f(') (I T)-lx whenever p(T) n D(f). If for all x in X nd all pairs f(1), (') of pro-ironing functions for x and T we have D .D then T is said to have the single-valued extension property. In this cse there is unique pre-imaging function with maximal domain p(x), al open set con- raining p(T). The values of this function re denoted by/x() e p(x)}.