Algebras generated by special symmetric polynomials on $\ell_1$

F. Jawad; H. Karpenko; A.V. Zagorodnyuk

doi:10.15330/cmp.11.2.335-344

F. Jawad Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
H. Karpenko Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
A.V. Zagorodnyuk Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-5554-4342

https://doi.org/10.15330/cmp.11.2.335-344

Keywords: symmetric and supersymmetric polynomials on Banach spaces, algebras of analytic functions on Banach spaces, spectra algebras of analytic functions

Published online: 2019-12-31

Abstract

Let $X$ be a weighted direct sum of infinity many copies of complex spaces $\ell_1\bigoplus \ell_1.$ We consider an algebra consisting of polynomials on $X$ which are supersymmetric on each term $\ell_1\bigoplus \ell_1.$ Point evaluation functionals on such algebra gives us a relation of equivalence `$\sim$' on $X.$ We investigate the quotient set $X/\sim$ and show that under some conditions, it has a real topological algebra structure.

Algebras generated by special symmetric polynomials on $\ell_1$

Abstract

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