A characterization of regular averaging operators and its consequences

• Autorzy: Spiros A. Argyros , Alexander D. Arvanitakis
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
• 28B20: Set-valued set functions and measures; integration of set-valued functions; measurable selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 151
• Numer: 3
• Strony: 207-226

Daty

wydano

2002

Twórcy

autor

Spiros A. Argyros

• Department of Mathematics, National Technical University of Athens, 15780 Athens, Greece

autor

Alexander D. Arvanitakis

• Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece

Identyfikatory

DOI

10.4064/sm151-3-2