拟保值域算子的一些应用

Some application of quasi--range--presening operator

本文给出了拟保值域算子的一些应用。

This paper proves the following results by quasi--range--preserving operator. （ 1 ）Let A. B be real （or complex）normed linear spaees,A { 0 } B4- { 0 }. A）be a bovnded subset of A which separtes the points ,of A, B;be a bounded subset of B＊ which separates the points of B. T be a linear operator sup α＋β（Tb） from B to A satisfies （x＊） ｜≤ suo ｜α＋βb（y）l xE A y＊E B V （., [3ER（orC）, bEB vbE B. ）the convex closed hull of b（BO） Then Tb （ A0 （2） Let X be a aompact spac% A be a subspace of CR （X）which ：ontains the constant functions, T be A to M（YR）, ｜｜T｜｜= 1, T1=1 a bounded linear operator from （i） Af, gEA, if f〈g then Tf〉Tg. （ii）If X is connected, then K（Tf）R（f）, A. （iii） If X is connected, A is a subalgebra of CR （X） f is invertible, then Tf is invertible.