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

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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.

**1.**R. B. Burckel,*Characterizations of 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*, 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****5.**K. Morita,*Dimension of general topological spaces*, Surveys in general topology (G. M. Reed ed.) Academic Press N. Y. 1980 MR**83b:54049**

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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