@article{Martsinkiv_Vasylyshyn_Vasylyshyn_Zagorodnyuk_2021, title={Lipschitz symmetric functions on Banach spaces with symmetric bases}, volume={13}, url={https://scijournals.pnu.edu.ua/index.php/cmp/article/view/5568}, DOI={10.15330/cmp.13.3.727-733}, abstractNote={<p>We investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_n|\le 1.$ Using functions $\max$ and $\min$ and tropical polynomials of several variables, we constructed a large family of Lipschitz symmetric functions on the Banach space $c_0$ which can be described as a semiring of compositions of tropical polynomials over $c_0$.</p>}, number={3}, journal={Carpathian Mathematical Publications}, author={Martsinkiv, M.V. and Vasylyshyn, S.I. and Vasylyshyn, T.V. and Zagorodnyuk, A.V.}, year={2021}, month={Dec.}, pages={727–733} }