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SYMMETRIC POLYNOMIALS ON REARRANGEMENT-INVARIANT FUNCTION SPACES

Published online by Cambridge University Press:  01 April 1999

MANUEL GONZÁLEZ ,
RAQUEL GONZALO  and
JESÚS ANGEL JARAMILLO
MANUEL GONZÁLEZ
Affiliation:
Facultad de Ciencias, Universidad de Cantabria, Avenida de los Castros s/n, 39071-Santander, Spain; [email protected]
RAQUEL GONZALO
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040-Madrid, Spain; [email protected], [email protected]
JESÚS ANGEL JARAMILLO
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040-Madrid, Spain; [email protected], [email protected]
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Abstract

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, [lscr ]2n, L2n[0, 1], L2n[0, ∞) and L2n[0, ∞)∩L2m[0, ∞) where n, m are both integers are the only spaces that admit separating polynomials.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 681 - 697
Copyright
The London Mathematical Society 1999

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