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ALGEBRAS OF SYMMETRIC HOLOMORPHIC FUNCTIONS ON ${\cal L}_p$

Published online by Cambridge University Press:  24 March 2003

RAYMUNDO ALENCAR ,
RICHARD ARON ,
PABLO GALINDO  and
ANDRIY ZAGORODNYUK
RAYMUNDO ALENCAR
Affiliation:
Instituto Tecnologico de Aeronautica, S.J. Campos, S.P., Brazilralencar@ief.ita.br
RICHARD ARON
Affiliation:
Department of Mathematics, Kent State University, Kent, OH 44242, USAaron@mcs.kent.edu
PABLO GALINDO
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), SpainPablo.Galindo@uv.es
ANDRIY ZAGORODNYUK
Affiliation:
Inst. for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3 b, Naukova Str., Lviv, Ukraine, 290601 sirand@mebm.lviv.ua
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Abstract

The authors study the algebra of uniformly continuous holomorphic symmetric functions on the ball of ${\cal L}_p$ , investigating in particular the spectrum of such algebras. To do so, they examine the algebra of symmetric polynomials on ${\cal L}_p$ -spaces, as well as finitely generated symmetric algebras of holomorphic functions. Such symmetric polynomials determine the points in ${\cal L}_p$ up to a permutation.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 1 , January 2003 , pp. 55 - 64
Copyright
© The London Mathematical Society 2003

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Footnotes

The first author was partially supported by FAPESP # 0004135 – 8. The work of the second author on this project started while he was a visitor in the Department of Mathematics at the Universidade de Coimbra, Portugal, to which sincere thanks are given. The third author was partially supported by DGESIC pr. no. P.B.96-0758. Finally, the work of the fourth author was supported in part by NSF Grant no. P-1-2089.