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
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] Andrew Browder, Introduction to function algebras, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0246125
  • [3] Andrew Browder and John Wermer, Some algebras of functions on an arc, J. Math. Mech. 12 (1963), 119–130. MR 0144223
  • [4] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523

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Additional Information

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