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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A holomorphic function having a discontinuous inverse


Author: T. J. Suffridge
Journal: Proc. Amer. Math. Soc. 31 (1972), 629-630
MathSciNet review: 0284813
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Abstract | References | Additional Information

Abstract: An example is given of a function $ f$ which is holomorphic in the open unit ball of $ {l^\infty }$ and which extends in a natural way to the closed unit ball. The extended function gives a one-toone correspondence of the closed ball with itself but the inverse function fails to be continuous on the image of the open ball under the map $ f$.


References [Enhancements On Off] (What's this?)

  • [1] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0284813-8
Keywords: Holomorphic function, holomorphic inverse, Banach space
Article copyright: © Copyright 1972 American Mathematical Society