Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra

  • S.I. Vasylyshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
https://doi.org/10.15330/cmp.15.1.104-119
Keywords: $n$-homogeneous polynomial, analytic function, spectrum of an algebra
Published online: 2023-06-20

Abstract


We consider the subalgebra of the Fréchet algebra of entire functions of bounded type, generated by a countable set of algebraically independent homogeneous polynomials on the complex Banach space $X.$ We investigate the spectrum of this subalgebra in the case $X = \ell_1.$ We also consider some shift type operations that can be performed on the spectrum of this subalgebra in the case $X = \ell_p$ with $p \geq 1$.

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How to Cite
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Vasylyshyn S. Spectra of Algebras of Analytic Functions, Generated by Sequences of Polynomials on Banach Spaces, and Operations on Spectra. Carpathian Math. Publ. 2023, 15 (1), 104-119.