Lipschitz symmetric functions on Banach spaces with symmetric bases
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DOI:
https://doi.org/10.15330/cmp.13.3.727-733Keywords:
Lipschitz symmetric function on Banach space, symmetric basis, tropical polynomialAbstract
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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2021-12-13
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Martsinkiv, M.; Vasylyshyn, S.; Vasylyshyn, T.; Zagorodnyuk, A. Lipschitz Symmetric Functions on Banach Spaces With Symmetric Bases: Array. Carpathian Math. Publ. 2021, 13, 727-733.
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Scientific articles