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Holomorphic maps of discs into balls of lp-spaces

Published online by Cambridge University Press:  24 October 2008

Josip Globevnik
Josip Globevnik
Affiliation:
Institute of Mathematics, Physics and Mechanics, E.K. University of Ljubljana, Yugoslavia
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Abstract

Let 1 ≤ p < ∞, let be the open unit ball of lp and let Δ be the open unit disc in ℂ. We prove that there is a holomorphic map such that F(Δ) is dense in and such that whenever .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 123 - 133
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Aron, R. M.. The range of vector-valued holomorphic mappings. Proc. Conf. Anal. Funct., Krakow, 1974. Ann. Polon. Math. 33 (1976), 17–20.CrossRefGoogle Scholar
[2]Aron, R. M. and Cima, J. A.. A theorem on holomorphic mappings into Banach spaces with basis. Proc. Amer. Math. Soc. 36 (1972), 289–292.Google Scholar
[3]Evgrafov, M. A.. Analytic Functions (Saunders, 1966).Google Scholar
[4]Globevnik, J.. Analytic functions whose range is dense in a ball. J. Funct. Anal. 22 (1976), 32–38.CrossRefGoogle Scholar
[5]Globevnik, J. and Stout, E. L.. The ends of varieties. To appear in Amer. J. Math.Google Scholar
[6]Hoffman, K.. Banach Spaces of Analytic Functions (Prentice-Hall, 1962).Google Scholar
[7]Nikolova-Dzhakova, V. L.. A holomorphic curve in the ball whose limit set contains the bounding sphere. Math. Notes 30 (1981), 537–541.CrossRefGoogle Scholar
[8]Rudin, W.. Holomorphic maps of discs into F-spaces. Complex Analysis, Kentucky 1976. Lecture Notes in Math. 599 (Springer-Verlag, 1977), pp. 104–108.Google Scholar
[9]Rudin, W.. Real and Complex Analysis (McGraw-Hill, 1966).Google Scholar
[10]Stout, E. L.. The Theory of Uniform Algebras (Bogden and Quigley, 1971).Google Scholar
[11]Zygmund, A.. Trigonometric Series (Cambridge University Press, 1959).Google Scholar