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Symmetric and finitely symmetric polynomials on the spaces ℓ ∞ and L ∞ [ 0 , + ∞ )
Author(s) -
Galindo Pablo,
Vasylyshyn Taras,
Zagorodnyuk Andriy
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700314
Subject(s) - bijection, injection and surjection , mathematics , invariant (physics) , pure mathematics , lebesgue measure , sequence (biology) , combinatorics , space (punctuation) , lebesgue integration , discrete mathematics , bijection , linguistics , philosophy , biology , mathematical physics , genetics
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 c 0 . The analogous study, with analogous results, is carried out onL ∞ [ 0 , + ∞ ) , replacing the permutations of N by measurable bijections of [ 0 , + ∞ ) that preserve the Lebesgue measure.