Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces

Christopher Boyd

Studia Mathematica (1993)

  • Volume: 107, Issue: 3, page 305-315
  • ISSN: 0039-3223

Abstract

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For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that G ( U ) i ' = ( ( U ) , τ δ ) . Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the τ 0 and τ ω topologies on ℋ (U).

How to cite

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Boyd, Christopher. "Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces." Studia Mathematica 107.3 (1993): 305-315. <http://eudml.org/doc/216035>.

@article{Boyd1993,
abstract = {For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that $G(U)^\{\prime \}_i = (ℋ (U),τ_δ)$. Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the $τ_0$ and $τ_ω$ topologies on ℋ (U).},
author = {Boyd, Christopher},
journal = {Studia Mathematica},
keywords = {Fréchet space},
language = {eng},
number = {3},
pages = {305-315},
title = {Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces},
url = {http://eudml.org/doc/216035},
volume = {107},
year = {1993},
}

TY - JOUR
AU - Boyd, Christopher
TI - Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces
JO - Studia Mathematica
PY - 1993
VL - 107
IS - 3
SP - 305
EP - 315
AB - For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that $G(U)^{\prime }_i = (ℋ (U),τ_δ)$. Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the $τ_0$ and $τ_ω$ topologies on ℋ (U).
LA - eng
KW - Fréchet space
UR - http://eudml.org/doc/216035
ER -

References

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