TY - JOUR
AU - Martsinkiv, M.V.
AU - Vasylyshyn, S.I.
AU - Vasylyshyn, T.V.
AU - Zagorodnyuk, A.V.
PY - 2021/12/13
Y2 - 2024/06/24
TI - Lipschitz symmetric functions on Banach spaces with symmetric bases
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://scijournals.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 -