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Proceedings of the American Mathematical Society

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

 
 

 

Compact $ 2$-manifolds as maximal ideal spaces


Author: Alfred G. Brandstein
Journal: Proc. Amer. Math. Soc. 41 (1973), 498-500
MSC: Primary 46J20
DOI: https://doi.org/10.1090/S0002-9939-1973-0324426-3
MathSciNet review: 0324426
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Abstract: It is shown that every compact $ 2$-manifold is (homeomorphic to) the maximal ideal space of an antisymmetric algebra which is Dirichlet on its Šilov boundary.


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

  • [1] A. G. Brandstein, Function spaces related to hypo-Dirichlet algebras, Doctoral Thesis, Brown University, Providence, R.I., 1972.
  • [2] A. Browder, Introduction to function algebras, Benjamin, New York, 1969. MR 39 #7431. MR 0246125 (39:7431)
  • [3] A. Browder and J. Wermer, Some algebras of functions on an arc, J. Math. Mech. 12 (1963), 119-130. MR 26 #1770. MR 0144223 (26:1770)
  • [4] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math. vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0324426-3
Keywords: $ 2$-manifold, Dirichlet
Article copyright: © Copyright 1973 American Mathematical Society

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