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Symmetric and finitely symmetric polynomials on the spaces ℓ∞ and L∞[0,+∞)

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  • Pablo Galindo
  • Taras Vasylyshyn
  • Andriy Zagorodnyuk

Abstract

We consider on the space ℓ∞ polynomials that are invariant regarding permutations of the sequence variable or regarding finite permutations. Accordingly, they are trivial or factor through c0. The analogous study, with analogous results, is carried out on L∞[0,+∞), replacing the permutations of N by measurable bijections of [0,+∞) that preserve the Lebesgue measure.

Suggested Citation

  • Pablo Galindo & Taras Vasylyshyn & Andriy Zagorodnyuk, 2018. "Symmetric and finitely symmetric polynomials on the spaces ℓ∞ and L∞[0,+∞)," Mathematische Nachrichten, Wiley Blackwell, vol. 291(11-12), pages 1712-1726, August.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:11-12:p:1712-1726
    DOI: 10.1002/mana.201700314
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