Abstract
LetB be a subgroup ofC(K) which separates points and contains the constants. An elementh∈C(R) operates onB iff∈B implies thath∘f∈B. An elementh∈C(R) is condensing if its operation onB implies the density ofB inC(K). Similar notation applies to subgroupsB ofC(K, G) whereG is a metrizable group. We study the setD(G) of condensing functions inC(G, G) whenG is the additive group of a real Banach space and in particular whenG=R n.
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Y. Sternfeld, Y. Weit (1988):An approximation theorem for vector-valued functions. In: Geometric Aspects of Functional Analysis (V. Milman, J. Lindenstrauss, eds.). Lecture Notes in Mathematics. Berlin: Springer-Verlag.
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Communicated by Huben Berens.AMS classification: 41A30.
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Sternfeld, Y. Dense subgroups ofC(K)-Stone-Weierstrass-type theorems for groups. Constr. Approx 6, 339–351 (1990). https://doi.org/10.1007/BF01888268
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DOI: https://doi.org/10.1007/BF01888268