@article{Vasylyshyn_2024, title={Algebras of symmetric and block-symmetric functions on spaces of Lebesgue measurable functions}, volume={16}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/8037}, DOI={10.15330/cmp.16.1.174-189}, abstractNote={<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>}, number={1}, journal={Carpathian Mathematical Publications}, author={Vasylyshyn, T.V.}, year={2024}, month={Jun.}, pages={174–189} }