Lipschitz symmetric functions on Banach spaces with symmetric bases
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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 $c_0$.
2020 ◽
Vol 12
(1)
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pp. 17-22
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2019 ◽
Vol 11
(1)
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pp. 42-47
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2010 ◽
Vol 82
(1)
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pp. 10-17
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