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Symmetric Polynomials on Rearrangement‐Invariant Function Spaces
Author(s) -
González Manuel,
Gonzalo Raquel,
Jaramillo Jesús Angel
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007164
Subject(s) - mathematics , invariant (physics) , pure mathematics , separable space , banach space , representation (politics) , discrete mathematics , mathematical analysis , mathematical physics , politics , political science , law
The exact representation of symmetric polynomials on Banach spaces with symmetric basis and also on separable rearrangement‐invariant function spaces over [0, 1] and [0, ∞) is given. As a consequence of this representation it is obtained that, among these spaces, l 2 n , L 2 n [0, 1], L 2 n [0, ∞) and L 2 n [0, ∞)∩ L 2 m [0, ∞) where n , m are both integers are the only spaces that admit separating polynomials.