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

Collectanea Mathematica (1991)

- Volume: 42, Issue: 3, page 237-243
- ISSN: 0010-0757

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topMerentes, Nelson. "On the Composition Operator in AC[a,b].." Collectanea Mathematica 42.3 (1991): 237-243. <http://eudml.org/doc/42539>.

@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 -

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