A Schottky-type theorem for starlike domains in Banach spaces
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- by Jorge Mujica and Paula Takatsuka PDF
- Proc. Amer. Math. Soc. 135 (2007), 1141-1144 Request permission
Abstract:
We show that if $U$ is a starlike domain in a Banach space $E$ and $\mathscr {F}$ is a family of holomorphic functions on $U$ that omit two distinct values and is bounded at the origin, then $\mathscr {F}$ is uniformly bounded on each $U$-bounded set.References
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Additional Information
- Jorge Mujica
- Affiliation: IMECC - UNICAMP, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
- Email: mujica@ime.unicamp.br
- Paula Takatsuka
- Affiliation: IMECC - UNICAMP, Caixa Postal 6065, 13083-970 Campinas, SP, Brazil
- Email: ptakatsu@ime.unicamp.br
- Received by editor(s): November 11, 2005
- Published electronically: October 11, 2006
- Additional Notes: The second author was supported by a teaching assistantship from UNICAMP
- Communicated by: Jonathan M. Borwein
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1141-1144
- MSC (2000): Primary 46G20, 46E50
- DOI: https://doi.org/10.1090/S0002-9939-06-08681-3
- MathSciNet review: 2262917