6533b82ffe1ef96bd12946ca

RESEARCH PRODUCT

New applications of extremely regular function spaces

Olav NygaardMärt PõldvereTrond A. Abrahamsen

subject

Mathematics::Functional AnalysisProperty (philosophy)Function spaceMathematics::Operator AlgebrasGeneral MathematicsHausdorff spaceTopological spaceLinear subspaceFunctional Analysis (math.FA)CombinatoricsMathematics - Functional AnalysisFOS: Mathematics46B20 46B22Locally compact spaceMathematicsReal number

description

Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$.

yearjournalcountryeditionlanguage
2017-11-04
10.2140/pjm.2019.301.385http://arxiv.org/abs/1711.01494