TY - JOUR AU - Martsinkiv, M.V. AU - Vasylyshyn, S.I. AU - Vasylyshyn, T.V. AU - Zagorodnyuk, A.V. PY - 2021/12/13 Y2 - 2024/03/28 TI - Lipschitz symmetric functions on Banach spaces with symmetric bases: Array JF - Carpathian Mathematical Publications JA - Carpathian Math. Publ. VL - 13 IS - 3 SE - Scientific articles DO - 10.15330/cmp.13.3.727-733 UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/5568 SP - 727-733 AB - <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> ER -