### Algebras generated by special symmetric polynomials on $\ell_1$

#### 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.

#### Keywords

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

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