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Some algebras of symmetric analytic functions and their spectra

Part of: Measures, integration, derivative, holomorphy Commutative Banach algebras and commutative topological algebras Linear function spaces and their duals

Published online by Cambridge University Press:  20 June 2011

Iryna Chernega ,
Pablo Galindo  and
Andriy Zagorodnyuk
Iryna Chernega
Affiliation:
Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3-b, Naukova str., Lviv 79060, Ukraine ([email protected])
Pablo Galindo
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Calle del Doctor Moliner 50, Burjasot, Valencia 46100, Spain ([email protected])
Andriy Zagorodnyuk
Affiliation:
Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., Ivano-Frankivsk 76000, Ukraine ([email protected])
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Abstract

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In the spectrum of the algebra of symmetric analytic functions of bounded type on ℓp, 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.

Keywords

Banach spacespolynomialssymmetric polynomialssymmetric and subsymmetric analytic functions of bounded typespectra of algebras

MSC classification

Secondary: 46J15: Banach algebras of differentiable or analytic functions, $H^p$-spaces 46J20: Ideals, maximal ideals, boundaries 46E15: Banach spaces of continuous, differentiable or analytic functions 46E25: Rings and algebras of continuous, differentiable or analytic functions 46G20: Infinite-dimensional holomorphy 46G25: (Spaces of) multilinear mappings, polynomials
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 125 - 142
Copyright
Copyright © Edinburgh Mathematical Society 2011

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