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Some algebras of symmetric analytic functions and their spectra

Published online by Cambridge University Press:  20 June 2011

Iryna Chernega
Affiliation:
Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3-b, Naukova str., Lviv 79060, Ukraine (icherneha@ukr.net)
Pablo Galindo
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Calle del Doctor Moliner 50, Burjasot, Valencia 46100, Spain (pablo.galindo@uv.es)
Andriy Zagorodnyuk
Affiliation:
Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., Ivano-Frankivsk 76000, Ukraine (andriyzag@yahoo.com)
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Abstract

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In the spectrum of the algebra of symmetric analytic functions of bounded type on p, 1 ≤ p < +∞, and along the same lines as the general non-symmetric case, we define and study a convolution operation and give a formula for the ‘radius’ function. It is also proved that the algebra of analytic functions of bounded type on ℓ1 is isometrically isomorphic to an algebra of symmetric analytic functions on a polydisc of ℓ1. We also consider the existence of algebraic projections between algebras of symmetric polynomials and the corresponding subspace of subsymmetric polynomials.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2011

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