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Supersymmetric Polynomials on the Space of Absolutely Convergent Series

Department of Mathematical and Functional Analysis, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
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Symmetry 2019, 11(9), 1111; https://doi.org/10.3390/sym11091111
Received: 10 July 2019 / Revised: 4 August 2019 / Accepted: 5 August 2019 / Published: 3 September 2019
We consider an algebra H b s u p of analytic functions on the Banach space of two-sided absolutely summing sequences which is generated by so-called supersymmetric polynomials. Our purpose is to investigate H b s u p and its spectrum with using methods of infinite dimensional complex analysis and the theory of Fréchet algebras. Some algebraic bases of H b s u p are described. Also, we show that the spectrum of the algebra of supersymmetric analytic functions of bounded type contains a metric ring M . We prove that M is a complete metric (nonlinear) space and investigate homomorphisms and additive operators on this ring. Some possible applications are discussed. View Full-Text
Keywords: symmetric and supersymmetric polynomials on Banach spaces; algebras of analytic functions on Banach spaces; spectra algebras of analytic functions symmetric and supersymmetric polynomials on Banach spaces; algebras of analytic functions on Banach spaces; spectra algebras of analytic functions
MDPI and ACS Style

Jawad, F.; Zagorodnyuk, A. Supersymmetric Polynomials on the Space of Absolutely Convergent Series. Symmetry 2019, 11, 1111. https://doi.org/10.3390/sym11091111

AMA Style

Jawad F, Zagorodnyuk A. Supersymmetric Polynomials on the Space of Absolutely Convergent Series. Symmetry. 2019; 11(9):1111. https://doi.org/10.3390/sym11091111

Chicago/Turabian Style

Jawad, Farah; Zagorodnyuk, Andriy. 2019. "Supersymmetric Polynomials on the Space of Absolutely Convergent Series" Symmetry 11, no. 9: 1111. https://doi.org/10.3390/sym11091111

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