Double commutants of multiplication operators on C(K).

2013/05/27 by Arkady Kitover, Kitover, Arkady
Mathematics · #47L10 #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47L10

paper · pdf · doi:10.48550/arxiv.1305.6286

8 pages

arxiv created 2013/05/27 · openalex publication_date 2013/05/27 · arxiv updated 2013/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C(K) be the space of all real or complex valued continuous functions on a compact Hausdorff space K. We are interested in the following property of K: for any real valued f ∈ C(K) the double commutant of the corresponding multiplication operator F coincides with the norm closed algebra generated by F and I. In this case we say that K ∈ DCP. It was proved in \citeKi that any locally connected metrizable continuum is in DCP. In this paper we indicate a class of arc connected but not locally connected continua that are in DCP. We also construct an example of a continuum that is not arc connected but is in DCP.

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