On the Composition Operator in AC[a,b].

@article{Merentes1991,
abstract = {Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.},
author = {Merentes, Nelson},
journal = {Collectanea Mathematica},
keywords = {Algebra de operadores; Funciones de variación acotada; Espacios de funciones; Aplicación lipschitziana; Composición; composition operator; space of absolutely continuous functions; local Lipschitz condition},
language = {eng},
number = {3},
pages = {237-243},
title = {On the Composition Operator in AC[a,b].},
url = {http://eudml.org/doc/42539},
volume = {42},
year = {1991},
}

TY - JOUR
AU - Merentes, Nelson
TI - On the Composition Operator in AC[a,b].
JO - Collectanea Mathematica
PY - 1991
VL - 42
IS - 3
SP - 237
EP - 243
AB - Denote by F the composition operator generated by a given function f: R --> R, acting on the space of absolutely continuous functions. In this paper we prove that the composition operator F maps the space AC[a,b] into itself if and only if f satisfies a local Lipschitz condition on R.
LA - eng
KW - Algebra de operadores; Funciones de variación acotada; Espacios de funciones; Aplicación lipschitziana; Composición; composition operator; space of absolutely continuous functions; local Lipschitz condition
UR - http://eudml.org/doc/42539
ER -