# Lipschitz symmetric functions on Banach spaces with symmetric bases

## Keywords:

Lipschitz symmetric function on Banach space, symmetric basis, tropical polynomial
Published online:
2021-12-13

### Abstract

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 $c_0$.

How to Cite

(1)

Martsinkiv, M.; Vasylyshyn, S.; Vasylyshyn, T.; Zagorodnyuk, A. Lipschitz Symmetric Functions on Banach Spaces With Symmetric Bases.

*Carpathian Math. Publ.***2021**,*13*, 727-733.