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

Annales Polonici Mathematici (1999)

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

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topDo 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

top- [1] A. Aytuna, The Fréchet space structure of global sections of certain coherent analytic sheaves, Math. Balkan. (N.S.) 3 (1989), 311-324. Zbl0712.46016
- [2] P. B. Djakov and B. S. Mitiagin, The structure of polynomial ideals in the algebra of entire functions, Studia Math. 68 (1980), 85-104. Zbl0434.46034
- [3] G. Fischer, Complex Analytic Geometry, Lecture Notes in Math. 538, Springer, 1976. Zbl0343.32002
- [4] H. Kazama and T. Umeno, ∂̅-cohomology of complex Lie groups, Publ. RIMS Kyoto Univ. 26 (1990), 473-484. Zbl0718.32018
- [5] J. Leiterer, Banach coherent sheaves, Math. Nachr. 85 (1978), 91-109. Zbl0409.32017
- [6] Y. Matsushima et A. Morimoto, Sur certains espaces fibrés holomorphes sur une variété de Stein, Bull. Soc. Math. France 88 (1960), 137-155. Zbl0094.28104
- [7] S. Takeuchi, On completeness of holomorphic principal bundles, Nagoya Math. J. 57 (1974), 121-138. Zbl0284.32020
- [8] D. Vogt, Subspaces and quotient spaces of (s), in: Functional Analysis: Surveys and Recent Results, K. D. Bierstedt and B. Fuchssteiner (eds.), North-Holland Math. Stud. 27, North-Holland, 1977, 168-187.
- [9] D. Vogt, Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen, Manuscripta Math. 37 (1982), 269-301. Zbl0512.46003
- [10] D. Vogt, Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist, J. Reine Angew. Math. 345 (1983), 182-200.
- [11] D. Vogt, Über die Existenz von Ausdehnungsoperatoren für holomorphe Funktionen auf analytischen Mengen in ${\u2102}^{n}$, preprint.
- [12] V. P. Zaharyuta, Isomorphism of spaces of analytic functions, Dokl. Akad. Nauk SSSR 225 (1980), 11-14 (in Russian); English transl.: Soviet Math. Dokl. 22 (1980), 631-634.

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