# Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces

Studia Mathematica (1991)

- Volume: 101, Issue: 1, page 83-104
- ISSN: 0039-3223

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topScheve, Manfred. "Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces." Studia Mathematica 101.1 (1991): 83-104. <http://eudml.org/doc/215894>.

@article{Scheve1991,

abstract = {Let Λ\_R(α) be a nuclear power series space of finite or infinite type with lim\_\{j→∞\} (1/j) log α\_j = 0. We consider open polydiscs D\_a in Λ\_R(α)'\_b with finite radii and the spaces H(D\_a) of all holomorphic functions on D\_a under the compact-open topology. We characterize all isomorphy classes of the spaces \{H(D\_a) | a ∈ Λ\_R(α), a > 0\}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory of linear operators between Fréchet spaces.},

author = {Scheve, Manfred},

journal = {Studia Mathematica},

keywords = {nuclear power series space of finite or infinite type; holomorphic functions; compact-open topology; linear operators between Fréchet spaces},

language = {eng},

number = {1},

pages = {83-104},

title = {Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces},

url = {http://eudml.org/doc/215894},

volume = {101},

year = {1991},

}

TY - JOUR

AU - Scheve, Manfred

TI - Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces

JO - Studia Mathematica

PY - 1991

VL - 101

IS - 1

SP - 83

EP - 104

AB - Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory of linear operators between Fréchet spaces.

LA - eng

KW - nuclear power series space of finite or infinite type; holomorphic functions; compact-open topology; linear operators between Fréchet spaces

UR - http://eudml.org/doc/215894

ER -

## References

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- [14] D. Vogt, Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist, J. Reine Angew. Math. 345 (1983), 182-200.
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- [16] V. P. Zakharyuta, Isomorphism and quasiequivalence of bases for Köthe power series spaces, in: Mathematical Programming and Related Problems (Proc. 7th Winter School, Drogobych 1974), Theory of Operators in Linear Spaces, Akad. Nauk SSSR, Tsentr. Ekon.-Mat. Inst., Moscow 1976, 101-126 (in Russian); see also Dokl. Akad. Nauk SSSR 221 (1975), 772-774 (in Russian).

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