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There do not exist minimal algebras between C*(X) and C(X) with prescribed real maximal ideal spaces

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Abstract

Let C(X) be the algebra of all real-valued continuous functions on a completely regular Hausdorff space X, and C*(X) the subalgebra of bounded functions. We prove that for any intermediate algebra A between C*(X) and C(X), other than C*(X), there exists a smaller intermediate algebra with the same real maximal ideals as in A. The space X is called A-compact if any real maximal ideal in A corresponds to a point in X. It follows that, for a noncompact space X, there does not exist any minimal intermediate algebra A for which A is A-compact. This completes the answer to a question raised by Redlin and Watson in 1987.

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References

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Authors and Affiliations

  1. Departamento De álgebra, Geometría y Topología, Facultad De Ciencias, Universidad De Valladolid, 47005, Valladolid, Spain

    J. M. Domínguez

  2. Departamento De Matemáticas, Universidad De León, 24071, León, Spain

    J. Gómez Pérez

Authors
  1. J. M. Domínguez
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  2. J. Gómez Pérez
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Domínguez, J.M., Pérez, J.G. There do not exist minimal algebras between C*(X) and C(X) with prescribed real maximal ideal spaces. Acta Mathematica Hungarica 94, 351–355 (2002). https://doi.org/10.1023/A:1015699730476

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  • DOI: https://doi.org/10.1023/A:1015699730476

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