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Point derivations of function algebras generated by holomorphic functions

Authors: R. G. M. Brummelhuis and P. J. de Paepe
Journal: Proc. Amer. Math. Soc. 105 (1989), 117-120
MSC: Primary 46J15
MathSciNet review: 933512
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Abstract: It is shown that a continuous point derivation on the algebra $ H(X)$ consisting of uniform limits on $ X$ of functions holomorphic in a neighborhood of a compact subset $ X$ in $ {{\mathbf{C}}^n}$, which vanishes on the polynomials is the trivial derivation.

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

  • [BdP] R. G. M. Brummelhuis and P. J. de Paepe, Derivations on algebras of holomorphic functions, Department of Math., Univ. of Amsterdam, Preprint Series 87-23, 1987 .
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  • [G2] Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR 0410387
  • [GR] Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
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Article copyright: © Copyright 1989 American Mathematical Society

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