Open AccessLipschitz symmetric functions on Banach spaces with symmetric bases
Author(s) -
Mariia Martsinkiv,
S.I. Vasylyshyn,
Taras Vasylyshyn,
Andriy Zagorodnyuk
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.3.727-733
Subject(s) - mathematics , lipschitz continuity , banach space , pure mathematics , symmetric function , space (punctuation) , combinatorics , philosophy , linguistics
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 $c_0$.