A characterization of regular averaging operators and its consequences
Volume 151 / 2002
Studia Mathematica 151 (2002), 207-226
MSC: Primary 46E15, 54C55; Secondary 28B20.
DOI: 10.4064/sm151-3-2
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 ${\cal C}$ 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.
