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On a characterization of the maximal
ideal spaces of commutative $C^*$-algebras
in which every element
is the square of another


Authors: Osamu Hatori and Takeshi Miura
Journal: Proc. Amer. Math. Soc. 128 (2000), 1185-1189
MSC (2000): Primary 46J10
DOI: https://doi.org/10.1090/S0002-9939-99-05454-4
Published electronically: September 30, 1999
MathSciNet review: 1690991
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Abstract | References | Similar Articles | Additional Information

Abstract: A topological condition is given for a locally connected compact Hausdorff space on which every complex-valued continuous function is the square of another. The condition need not be necessary nor sufficient unless the space is locally connected.


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

  • 1. R. B. Burckel, Characterizations of $C(X)$ among its subalgebras, Marcel Dekker, N. Y. 1972 MR 56:1068
  • 2. E. M. \v{C}irka, Approximation of continuous functions by functions holomorphic on Jordan arcs in $\mathbb{C}^n$, Soviet Math. 7 (1966), pp. 1-99.
  • 3. R. Engelking, Outline of general topology, North-Holland, Amsterdam, 1968 MR 37:5836
  • 4. T. W. Gamelin, Uniform algebras, Prentice-Hall, N. J. 1969 MR 53:14137
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Additional Information

Osamu Hatori
Affiliation: Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no-chou, Niigata 950-21, Japan

Takeshi Miura
Affiliation: Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no-chou, Niigata 950-21, Japan

DOI: https://doi.org/10.1090/S0002-9939-99-05454-4
Keywords: Commutative Banach algebras, maximal ideal spaces
Received by editor(s): February 20, 1998
Received by editor(s) in revised form: June 17, 1998
Published electronically: September 30, 1999
Additional Notes: The first author was supported in part by the Grants in Aid for Scientific Research, The Ministry of Education, Science and Culture, Japan
Dedicated: Dedicated to Professor Junzo Wada on his seventieth birthday
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society

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