Lipschitz symmetric functions on Banach spaces with symmetric bases

  • M.V. Martsinkiv Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • S.I. Vasylyshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • T.V. Vasylyshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • A.V. Zagorodnyuk Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
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 $c_0$.

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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 (3), 727-733.

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