Abstract
For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology τγ on the space \(H\left( {U,F} \right)\) of holomorphic functions from U into F. This topology allows us to construct a predual for \(\left( {H\left( {U,F} \right),\tau \delta } \right)\) which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions.
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Boyd, C. Preduals of Spaces of Vector-Valued Holomorphic Functions. Czechoslovak Mathematical Journal 53, 365–376 (2003). https://doi.org/10.1023/A:1026287320596
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DOI: https://doi.org/10.1023/A:1026287320596