# The algebra of symmetric polynomials on $(L_\infty)^n$

Author
Vasyl Stefanyk Precarpathian National University, Ukraine
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 $n$th Cartesian power of the complex Banach space $L_\infty$ 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 $n$th Cartesian power of $L_\infty.$
Keywords
polynomial; symmetric polynomial; algebraic combination; algebraic basis
DOI
doi:10.30970/ms.52.1.71-85
Reference
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Pages
71-85
Volume
52
Issue
1
Year
2019
Journal
Matematychni Studii
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