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Proceedings of the American Mathematical Society

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An isolated bounded point derivation


Author: Anthony G. O’Farrell
Journal: Proc. Amer. Math. Soc. 39 (1973), 559-562
MSC: Primary 46J10
DOI: https://doi.org/10.1090/S0002-9939-1973-0315452-9
MathSciNet review: 0315452
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Abstract: For a compact subset $ X$ of the plane, $ R(X)$ denotes the class of uniform limits on $ X$ of rational functions with poles off $ X$. $ R(X)$ is a function algebra on $ X$. An example $ X$ is constructed such that $ R(X)$ admits a bounded point derivation at exactly one point of $ X$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0315452-9
Keywords: Bounded point derivation, uniform norm, Swiss Cheese
Article copyright: © Copyright 1973 American Mathematical Society

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