We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain a new characterization of Eberlein compact sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-3-2,
author = {Spiros A. Argyros and Alexander D. Arvanitakis},
title = {A characterization of regular averaging operators and its consequences},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {207-226},
zbl = {1027.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-3-2}
}
Spiros A. Argyros; Alexander D. Arvanitakis. A characterization of regular averaging operators and its consequences. Studia Mathematica, Tome 151 (2002) pp. 207-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-3-2/