On the inverse function theorem: A counterexample

Warren, Hugh E.

doi:10.1090/S0002-9939-1973-0312262-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the inverse function theorem: A counterexample
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by Hugh E. Warren PDF

Proc. Amer. Math. Soc. 38 (1973), 434-435 Request permission

Abstract:

The inverse function theorem for analytic functions has a generalization to $C(X)$ which fails in the disk algebra.

References

Lars V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, 2nd ed., McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0188405
Barnett W. Glickfeld, On the inverse function theorem in commutative Banach algebras, Illinois J. Math. 15 (1971), 212–221. MR 273408
Edgar R. Lorch, The theory of analytic functions in normed Abelian vector rings, Trans. Amer. Math. Soc. 54 (1943), 414–425. MR 9090, DOI 10.1090/S0002-9947-1943-0009090-0