Approximations of Symmetric Functions on Banach Spaces with Symmetric Bases
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This paper is devoted to studying approximations of symmetric continuous functions by symmetric analytic functions on a Banach space X with a symmetric basis. We obtain some positive results for the case when X admits a separating polynomial using a symmetrization operator. However, even in this case, there is a counter-example because the symmetrization operator is well defined only on a narrow, proper subspace of the space of analytic functions on X. For X=c0, we introduce ε-slice G-analytic functions that have a behavior similar to G-analytic functions at points x∈c0 such that all coordinates of x are greater than ε, and we prove a theorem on approximations of uniformly continuous functions on c0 by ε-slice G-analytic functions.
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2001 ◽
Vol 33
(6)
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pp. 715-726
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2013 ◽
Vol 160
(1)
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pp. 50-55
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2005 ◽
Vol 45
(1)
◽
pp. 84-93
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2012 ◽
Vol 2012
◽
pp. 1-21
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