Geodesic
A characterization of regular averaging operators and its consequences
Spiros A. Argyros 1   ; Alexander D. Arvanitakis 2
1 Department of Mathematics National Technical University of Athens 15780 Athens, Greece
2 Department of Mathematics University of Athens Panepistimiopolis 15784 Athens, Greece
Studia Mathematica, Tome 151 (2002) no. 3, pp. 207-226 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${\cal C}$ to $[0,1]$ admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from ${\cal C}$ 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.
DOI : 10.4064/sm151-3-2
Keywords: present characterization continuous surjections between compact metric spaces admitting regular averaging operator among its consequences concrete continuous surjections cantor set cal admitting regular averaging operators exhibited moreover set type continuous surjections cal dense supremum norm set continuous surjections non metrizable investigated consequence obtain characterization eberlein compact sets

Spiros A. Argyros  1   ; Alexander D. Arvanitakis  2

1 Department of Mathematics National Technical University of Athens 15780 Athens, Greece
2 Department of Mathematics University of Athens Panepistimiopolis 15784 Athens, Greece 
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Spiros A. Argyros; Alexander D. Arvanitakis. A characterization of regular averaging operators
 and its consequences. Studia Mathematica, Tome 151 (2002) no. 3, pp. 207-226. doi: 10.4064/sm151-3-2

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