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

Pablo Galindo, Taras Vasylyshyn and Andriy Zagorodnyuk

Mathematische Nachrichten, 2018, vol. 291, issue 11-12, 1712-1726

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.

Date: 2018
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