Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T14:21:59.660Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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