On a characterization of the maximal
ideal spaces of commutative 
-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
Full-text PDF Free Access
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.
- 1. R. B. Burckel, Characterizations of 𝐶(𝑋) among its subalgebras, Marcel Dekker, Inc., New York, 1972. Lecture Notes in Pure and Applied Mathematics, Vol. 6. MR 0442687
- 2.
E. M. \v{C}irka, Approximation of continuous functions by functions holomorphic on Jordan arcs in
, Soviet Math. 7 (1966), pp. 1-99.
- 3. R. Engelking, Outline of general topology, Translated from the Polish by K. Sieklucki, North-Holland Publishing Co., Amsterdam; PWN-Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. MR 0230273
- 4. Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR 0410387
- 5. Kiiti Morita, Dimension of general topological spaces, Surveys in general topology, Academic Press, New York-London-Toronto, Ont., 1980, pp. 297–336. MR 564105
among its subalgebras, Marcel Dekker, N. Y. 1972 Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46J10
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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
