Isomorphisms of AC(σ) spaces

Ian Doust, and Michael Leinert. "Isomorphisms of AC(σ) spaces." Studia Mathematica 228.1 (2015): 7-31. <http://eudml.org/doc/285834>.

@article{IanDoust2015,
abstract = {Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple polygons.},
author = {Ian Doust, Michael Leinert},
journal = {Studia Mathematica},
keywords = {absolutely continuous functions; algebraic isomorphism; Banach-Stone theorem},
language = {eng},
number = {1},
pages = {7-31},
title = {Isomorphisms of AC(σ) spaces},
url = {http://eudml.org/doc/285834},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Ian Doust
AU - Michael Leinert
TI - Isomorphisms of AC(σ) spaces
JO - Studia Mathematica
PY - 2015
VL - 228
IS - 1
SP - 7
EP - 31
AB - Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple polygons.
LA - eng
KW - absolutely continuous functions; algebraic isomorphism; Banach-Stone theorem
UR - http://eudml.org/doc/285834
ER -