Holomorphic germs on Banach spaces

Chae Soo Bong

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 3, page 107-141
  • ISSN: 0373-0956

Abstract

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Let E and F be two complex Banach spaces, U a nonempty subset of E and K a compact subset of E . The concept of holomorphy type θ between E and F , and the natural locally convex topology 𝒯 ω , θ on the vector space ℋ θ ( U , F ) of all holomorphic mappings of a given holomorphy type θ from U to F were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space ℋ θ ( K , F ) of all germs of holomorphic mappings into F around K of a given holomorphy type θ , and study its interplay with ℋ θ ( U , F ) and some other properties of the topology 𝒯 ω , θ .

How to cite

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Chae Soo Bong. "Holomorphic germs on Banach spaces." Annales de l'institut Fourier 21.3 (1971): 107-141. <http://eudml.org/doc/74041>.

@article{ChaeSooBong1971,
abstract = {Let $E$ and $F$ be two complex Banach spaces, $U$ a nonempty subset of $E$ and $K$ a compact subset of $E$. The concept of holomorphy type $\theta $ between $E$ and $F$, and the natural locally convex topology $\{\cal T\}_\{\omega ,\theta \}$ on the vector space $\{\cal H\}_\theta (U,F)$ of all holomorphic mappings of a given holomorphy type $\theta $ from $U$ to $F$ were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space $\{\cal H\}_\theta (K,F)$ of all germs of holomorphic mappings into $F$ around $K$ of a given holomorphy type $\theta $, and study its interplay with $\{\cal H\}_\theta (U,F)$ and some other properties of the topology $\{\cal T\}_\{\omega ,\theta \}$.},
author = {Chae Soo Bong},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {107-141},
publisher = {Association des Annales de l'Institut Fourier},
title = {Holomorphic germs on Banach spaces},
url = {http://eudml.org/doc/74041},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Chae Soo Bong
TI - Holomorphic germs on Banach spaces
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 3
SP - 107
EP - 141
AB - Let $E$ and $F$ be two complex Banach spaces, $U$ a nonempty subset of $E$ and $K$ a compact subset of $E$. The concept of holomorphy type $\theta $ between $E$ and $F$, and the natural locally convex topology ${\cal T}_{\omega ,\theta }$ on the vector space ${\cal H}_\theta (U,F)$ of all holomorphic mappings of a given holomorphy type $\theta $ from $U$ to $F$ were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space ${\cal H}_\theta (K,F)$ of all germs of holomorphic mappings into $F$ around $K$ of a given holomorphy type $\theta $, and study its interplay with ${\cal H}_\theta (U,F)$ and some other properties of the topology ${\cal T}_{\omega ,\theta }$.
LA - eng
UR - http://eudml.org/doc/74041
ER -

References

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