Characterizations and Extensions of Lipschitz-α Operators
Characterizations and Extensions of Lipschitz-α Operators作者机构:College of Mathematics and Information ScienceShaanxi Normal University Faculty of ScienceXi'an Jiaotong University
出 版 物:《Acta Mathematica Sinica,English Series》 (数学学报(英文版))
年 卷 期:2006年第22卷第3期
页 面:671-678页
核心收录:
学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金:partly supported by NNSF of China(No.19771056 No.69975016 No.10561113)
主 题:Characterization Extension Lipschitz-α operator
摘 要:In this work, we prove that a map F from a compact metric space K into a Banach space X over F is a Lipschitz-α operator if and only if for each σ in X^* the map σoF is a Lipschitz-α function on K. In the case that K = [a, b], we show that a map f from [a, b] into X is a Lipschitz-1 operator if and only if it is absolutely continuous and the map σ→ (σ o f)' is a bounded linear operator from X^* into L^∞([a, b]). When K is a compact subset of a finite interval (a, b) and 0 〈 α ≤ 1, we show that every Lipschitz-α operator f from K into X can be extended as a Lipschitz-α operator F from [a, b] into X with Lα(f) ≤ Lα(F) ≤ 3^1-α Lα(f). A similar extension theorem for a little Lipschitz-α operator is also obtained.