Double commutants of multiplication operators on $C(K).$

zbMATH Open1342.47048arXiv1305.6286MaRDI QIDQ5416038

Arkady Kitover

Publication date: 19 May 2014

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 $finC(K)$ 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 $KinmathcalDCP$. It was proved in cite{Ki} that any locally connected metrizable continuum is in $mathcalDCP$. In this paper we indicate a class of arc connected but not locally connected continua that are in $mathcalDCP$. We also construct an example of a continuum that is not arc connected but is in $mathcalDCP$.

Full work available at URL: https://arxiv.org/abs/1305.6286

zbMATH Keywords

multiplication operatordouble commutantcompact metrizable arc connected continuum

Mathematics Subject Classification ID

Linear operators on function spaces (general) (47B38) Linear operators on Banach algebras (47B48)

Related Items (2)

Structure of the operators that commute twice with operators of class K(H) ⋮ On the double commutant of Cowen-Douglas operators

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