A characterization of regular averaging operators and its consequences

Spiros A. Argyros; Alexander D. Arvanitakis

Studia Mathematica (2002)

  • Volume: 151, Issue: 3, page 207-226
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Spiros A. Argyros, and Alexander D. Arvanitakis. "A characterization of regular averaging operators and its consequences." Studia Mathematica 151.3 (2002): 207-226. <http://eudml.org/doc/284508>.

@article{SpirosA2002,
abstract = {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.},
author = {Spiros A. Argyros, Alexander D. Arvanitakis},
journal = {Studia Mathematica},
keywords = {averaging operator; Ditor space; Eberlein compact; Milyutin theorem; totally disconnected compact},
language = {eng},
number = {3},
pages = {207-226},
title = {A characterization of regular averaging operators and its consequences},
url = {http://eudml.org/doc/284508},
volume = {151},
year = {2002},
}

TY - JOUR
AU - Spiros A. Argyros
AU - Alexander D. Arvanitakis
TI - A characterization of regular averaging operators and its consequences
JO - Studia Mathematica
PY - 2002
VL - 151
IS - 3
SP - 207
EP - 226
AB - 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.
LA - eng
KW - averaging operator; Ditor space; Eberlein compact; Milyutin theorem; totally disconnected compact
UR - http://eudml.org/doc/284508
ER -

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