Preduals of spaces of vector-valued holomorphic functions

Christopher Boyd

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 2, page 365-376
  • ISSN: 0011-4642

Abstract

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For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology τ γ on the space ℋ ( U , F ) of holomorphic functions from U into F . This topology allows us to construct a predual for ( ℋ ( U , F ) , τ δ ) 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.

How to cite

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Boyd, Christopher. "Preduals of spaces of vector-valued holomorphic functions." Czechoslovak Mathematical Journal 53.2 (2003): 365-376. <http://eudml.org/doc/30783>.

@article{Boyd2003,
abstract = {For $U$ a balanced open subset of a Fréchet space $E$ and $F$ a dual-Banach space we introduce the topology $\tau _\gamma $ on the space $\{\mathcal \{H\}\}(U,F)$ of holomorphic functions from $U$ into $F$. This topology allows us to construct a predual for $(\{\mathcal \{H\}\}(U,F),\tau _\delta )$ 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.},
author = {Boyd, Christopher},
journal = {Czechoslovak Mathematical Journal},
keywords = {holomorphic functions; Fréchet spaces; preduals; holomorphic functions; Fréchet spaces; preduals},
language = {eng},
number = {2},
pages = {365-376},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Preduals of spaces of vector-valued holomorphic functions},
url = {http://eudml.org/doc/30783},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Boyd, Christopher
TI - Preduals of spaces of vector-valued holomorphic functions
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 365
EP - 376
AB - For $U$ a balanced open subset of a Fréchet space $E$ and $F$ a dual-Banach space we introduce the topology $\tau _\gamma $ on the space ${\mathcal {H}}(U,F)$ of holomorphic functions from $U$ into $F$. This topology allows us to construct a predual for $({\mathcal {H}}(U,F),\tau _\delta )$ 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.
LA - eng
KW - holomorphic functions; Fréchet spaces; preduals; holomorphic functions; Fréchet spaces; preduals
UR - http://eudml.org/doc/30783
ER -

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