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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## A characterization of regular averaging operators and its consequences

### Tom 151 / 2002

Studia Mathematica 151 (2002), 207-226 MSC: Primary 46E15, 54C55; Secondary 28B20. DOI: 10.4064/sm151-3-2

#### Streszczenie

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.

#### Autorzy

• Spiros A. ArgyrosDepartment of Mathematics
National Technical University of Athens
15780 Athens, Greece
e-mail
• Alexander D. ArvanitakisDepartment of Mathematics
University of Athens
Panepistimiopolis
15784 Athens, Greece
e-mail

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