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
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
Martsinkiv M., Vasylyshyn S., Vasylyshyn T., Zagorodnyuk A. Lipschitz Symmetric Functions on Banach Spaces With Symmetric Bases. Carpathian Math. Publ. 2021, 13 (3), 727-733.