Isometries on spaces of absolutely continuous functions in a noncompact framework

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Hosseini, Maliheh¹  Font, Juan J.² 

[1] KN Toosi Univ Technol, Fac Math, Tehran 163151618, Iran

[2] Univ Jaume 1, Dept Matemat, Campus Riu Sec,8029 AP, Castellon de La Plana, Spain

关键词: Isometry;    Absolutely continuous functions;    Stone-Cech compactification;    Weighted composition operators;   

DOI  :  10.1016/j.jmaa.2020.123962

来源: Elsevier

【 摘 要 】

In this paper we deal with surjective linear isometries between spaces of scalar-valued absolutely continuous functions on arbitrary (not necessarily closed or bounded) subsets of the real line (with at least two points). As a corollary, it is shown that when the underlying spaces are connected, each surjective linear isometry of these function spaces is a weighted composition operator, a result which generalizes all the previous known results concerning such isometries. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free