The algebra of symmetric polynomials on (L∞)n
Journal Title: Математичні Студії - Year 2019, Vol 52, Issue 1
Abstract
The paper deals with continuous symmetric (invariant under composition of the variable with any measure preserving bijection of [0,1]) complex-valued polynomials on the nth Cartesian power of the complex Banach space L∞ of all Lebesgue measurable essentially bounded complex-valued functions on [0,1]. We construct an algebraic basis of the algebra of all such polynomials. Results of the paper can be used for investigations of algebras of symmetric continuous polynomials and of symmetric analytic functions on the nth Cartesian power of L∞.
Authors and Affiliations
T. V. Vasylyshyn
Keywords
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- EP ID EP673810
- DOI 10.30970/ms.52.1.71-85
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