A structure of ring homomorphisms on commutative Banach algebras
Authors:
SinEi Takahasi and Osamu Hatori
Journal:
Proc. Amer. Math. Soc. 127 (1999), 22832288
MSC (1991):
Primary 46J05, 46E25
Published electronically:
April 9, 1999
MathSciNet review:
1486754
Fulltext PDF Free Access
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Abstract: We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that:  (i)
 A ring homomorphism of a commutative algebra onto another commutative algebra with connected infinite Gelfand space is either linear or antilinear.
 (ii)
 A ring automorphism of is either linear or antilinear.
 (iii)
 , and the disc algebra are neither ring homomorphic images of nor .
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Additional Information
SinEi Takahasi
Affiliation:
Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 9928510, Japan
Osamu Hatori
Affiliation:
Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata 9502102, Japan
Email:
hatori@math.sc.niigatau.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993999048194
PII:
S 00029939(99)048194
Keywords:
Commutative Banach algebra,
ring homomorphism,
Gelfand transform,
Fourier transform
Received by editor(s):
May 29, 1997
Received by editor(s) in revised form:
October 27, 1997
Published electronically:
April 9, 1999
Additional Notes:
The authors are partly supported by the GrantsinAid for Scientific Research, The Ministry of Education, Science and Culture, Japan
Dedicated:
Dedicated to Professor Jyunji Inoue on his sixtieth birthday
Communicated by:
David R. Larson
Article copyright:
© Copyright 1999
American Mathematical Society
