Holomorphic germs on certain locally convex spaces |
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Authors: | Roberto Luiz Soraggi |
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Institution: | (1) Present address: Instituto de Matematica, Universidad Federal de Rio de Janeiro, Caixa postal 68530, CEP 21944 Rio de Janeiro, R.J., Brazil |
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Abstract: | Summary
We study the bounded sets in the space of holomorphic germs defined on compact subsets of non-metrizable locally convex spaces. We relate this problem to the problem of existence of uniform Cauchy estimates for the bounded subsets. We show that the space of holomorphic germs defined on a compact subset of a reflexive dual Fréchet space is regular if the bounded subsets of the space of holomorphic germs defined at the origin have uniform Cauchy estimates. |
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