Frechet spaces of non-archimedean valued continuous functions
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Date
2012
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Abstract
Let $X$ be an ultraregular space and let $K$ be a complete non-archimedean
non-trivially valued field. Assume that the locally convex space $E$ = $C_c(X;K)$
of all continuous functions from $X$ to $K$ with the topology of uniform
convergence on compact subsets of $X$ is a Frechet space. We shall prove that
$E$ has an orthogonal basis consisting of $K$-valued characteristic functions of
clopen (i.e. closed and open) subsets of $X$ and that it is isomorphic to the
product of a countable family of Banach spaces with an orthonormal basis.
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The National Center of Science, Poland (grant no. N N201 605340)
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Citation
J. Math. Anal. Appl., 385(2012), 345-353