Karpatsʹkì Matematičnì Publìkacìï (Jun 2023)

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

  • S.I. Vasylyshyn

DOI
https://doi.org/10.15330/cmp.15.1.104-119
Journal volume & issue
Vol. 15, no. 1
pp. 104 – 119

Abstract

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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 $p \geq 1$.

Keywords