Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group

Do Duc Thai; Dinh Huy Hoang

Annales Polonici Mathematici (1999)

  • Volume: 71, Issue: 2, page 105-111
  • ISSN: 0066-2216

Abstract

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We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection π 1 : V → Γ is finite and proper, then R V : O ( Γ × G ) → I m R V ⊂ O ( V ) has a right inverse

How to cite

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Do Duc Thai, and Dinh Huy Hoang. "Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group." Annales Polonici Mathematici 71.2 (1999): 105-111. <http://eudml.org/doc/262831>.

@article{DoDucThai1999,
abstract = {We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection $π_1 : V → Γ$ is finite and proper, then $R_V : O(Γ × G) → Im R_V ⊂ O(V)$ has a right inverse},
author = {Do Duc Thai, Dinh Huy Hoang},
journal = {Annales Polonici Mathematici},
keywords = {complex Lie group; linear topological invariant; right inverse; extension operator; holomorphic functions; complex Lie groups; Fréchet spaces of holomorphic functions; bounded plurisubharmonic function},
language = {eng},
number = {2},
pages = {105-111},
title = {Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group},
url = {http://eudml.org/doc/262831},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Do Duc Thai
AU - Dinh Huy Hoang
TI - Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 2
SP - 105
EP - 111
AB - We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection $π_1 : V → Γ$ is finite and proper, then $R_V : O(Γ × G) → Im R_V ⊂ O(V)$ has a right inverse
LA - eng
KW - complex Lie group; linear topological invariant; right inverse; extension operator; holomorphic functions; complex Lie groups; Fréchet spaces of holomorphic functions; bounded plurisubharmonic function
UR - http://eudml.org/doc/262831
ER -

References

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  11. [11] D. Vogt, Über die Existenz von Ausdehnungsoperatoren für holomorphe Funktionen auf analytischen Mengen in ℂ n , preprint. 
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