TY - JOUR
AU - Vasylyshyn, T.V.
PY - 2024/06/06
Y2 - 2024/11/09
TI - Algebras of symmetric and block-symmetric functions on spaces of Lebesgue measurable functions
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 16
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.16.1.174-189
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/8037
SP - 174-189
AB - <p>In this work, we investigate algebras of symmetric and block-symmetric polynomials and analytic functions on complex Banach spaces of Lebesgue measurable functions for which the $p$th power of the absolute value is Lebesgue integrable, where $p\in[1,+\infty),$ and Lebesgue measurable essentially bounded functions on $[0,1]$. We show that spectra of Fréchet algebras of block-symmetric entire functions of bounded type on these spaces consist only of point-evaluation functionals. Also we construct algebraic bases of algebras of continuous block-symmetric polynomials on these spaces. We generalize the above-mentioned results to a wide class of algebras of symmetric entire functions.</p>
ER -