Note on separately symmetric polynomials on the Cartesian product of $\ell_1$

Author
F. Jawad
Vasyl Stefanyk Precarpathian National University Ivano-Frankivsk, Ukraine
Abstract
In the paper, we describe algebraic bases in algebras of separately symmetric polynomials which are defined on Cartesian products of $n$ copies of $\ell_1.$ Also, we describe spectra of algebras of entire functions, generated by these polynomials as Cartesian products of spectra of algebras of symmetric analytic functions of bounded type on $\ell_1.$ Finally, we consider algebras of separately symmetric analytic functions of bounded type on infinite direct sums of copies of $\ell_1.$ In particular, we show that there is a homomorphism from such algebra onto the algebra of all analytic functions of bounded type on a Banach space $X$ with an unconditional basis.
Keywords
polynomials and analytic functions on Banach spaces; symmetric analytic functions; block-symmetric polynomials; separately symmetric polynomials
DOI
doi:10.15330/ms.50.2.204-210
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Pages
204-210
Volume
50
Issue
2
Year
2018
Journal
Matematychni Studii
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