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Displaying similar documents to “Almost regular operators are regular.”

A characterization of regular averaging operators and its consequences

Spiros A. Argyros, Alexander D. Arvanitakis (2002)

Studia Mathematica

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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,...