The range of a ring homomorphism from a commutative algebra
Author:
Lajos Molnár
Journal:
Proc. Amer. Math. Soc. 124 (1996), 17891794
MSC (1991):
Primary 46J05, 46E25
MathSciNet review:
1307551
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Abstract: We prove that if a commutative semisimple Banach algebra is the range of a ring homomorphism from a commutative algebra, then is equivalent, i.e. there are a commutative algebra and a bicontinuous algebra isomorphism between and . In particular, it is shown that the group algebras , and the disc algebra are not ring homomorphic images of algebras.
 [Bur]
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
(56 #1068)
 [Cro]
R.
W. Cross, On the continuous linear image of a Banach space, J.
Austral. Math. Soc. Ser. A 29 (1980), no. 2,
219–234. MR
566287 (81f:47001)
 [Cun]
Joachim
Cuntz, Locally 𝐶*equivalent algebras, J. Functional
Analysis 23 (1976), no. 2, 95–106. MR 0448088
(56 #6398)
 [FD]
J.
M. G. Fell and R.
S. Doran, Representations of *algebras, locally compact groups,
and Banach *algebraic bundles. Vol. 1, Pure and Applied Mathematics,
vol. 125, Academic Press, Inc., Boston, MA, 1988. Basic representation
theory of groups and algebras. MR 936628
(90c:46001)
 [FW]
P.
A. Fillmore and J.
P. Williams, On operator ranges, Advances in Math.
7 (1971), 254–281. MR 0293441
(45 #2518)
 [Kuc]
Marek
Kuczma, An introduction to the theory of functional equations and
inequalities, Prace Naukowe Uniwersytetu Śląskiego w
Katowicach [Scientific Publications of the University of Silesia],
vol. 489, Uniwersytet Śląski, Katowice; Państwowe
Wydawnictwo Naukowe (PWN), Warsaw, 1985. Cauchy’s equation and
Jensen’s inequality; With a Polish summary. MR 788497
(86i:39008)
 [Mol]
L. Molnár, Algebraic difference between classes of an algebra, Proc. Amer. Math. Soc. (to appear). CMP 94:17
 [Pal]
Theodore
W. Palmer, Banach algebras and the general theory of *algebras.
Vol. I, Encyclopedia of Mathematics and its Applications,
vol. 49, Cambridge University Press, Cambridge, 1994. Algebras and
Banach algebras. MR 1270014
(95c:46002)
 [Rud]
W. Rudin, Real and Complex Analysis, Tata McGrawHill Publishing Co. Ltd., New Delhi, 1983.
 [Bur]
 R.B. Burckel, Characterization of among Its Subalgebras, Lecture Notes in Pure Appl. Math. 6, Marcel Dekker, 1972. MR 56:1068
 [Cro]
 R.W. Cross, On the continuous linear image of a Banach space, J. Austral. Math. Soc. (Series A) 29 (1980), 219234. MR 81f:47001
 [Cun]
 J. Cuntz, Locally equivalent algebras, J. Funct. Anal. 23 (1976), 95106. MR 56:6398
 [FD]
 J.M.G. Fell and R.S. Doran, Representations of *Algebras, Locally Compact Groups, and Banach *Algebraic Bundles, Vol. I., Academic Press, 1988. MR 90c:46001
 [FW]
 P.A. Fillmore and J.P. Williams, On operator ranges, Adv. Math. 7 (1971), 254281. MR 45:2518
 [Kuc]
 M. Kuczma, An Introduction to The Theory of Functional Equations and Inequalities, Pa\'{n}stwowe Wydawnictwo Naukowe, Warszawa, 1985. MR 86i:39008
 [Mol]
 L. Molnár, Algebraic difference between classes of an algebra, Proc. Amer. Math. Soc. (to appear). CMP 94:17
 [Pal]
 T. W. Palmer, Banach Algebras and The General Theory of *Algebras, Vol. I., Encyclopedia Math. Appl. 49, Cambridge University Press, 1994. MR 95c:46002
 [Rud]
 W. Rudin, Real and Complex Analysis, Tata McGrawHill Publishing Co. Ltd., New Delhi, 1983.
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Additional Information
Lajos Molnár
Affiliation:
Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O.Box 12, Hungary
Email:
molnarl@math.klte.hu
DOI:
http://dx.doi.org/10.1090/S0002993996032364
PII:
S 00029939(96)032364
Keywords:
Ring homomorphism,
commutative Banach algebra,
Gelfand representation
Received by editor(s):
November 21, 1994
Additional Notes:
Research partially supported by the Hungarian National Research Science Foundation, Operating Grant Number OTKA 1652 and K&H Bank Ltd., Universitas Foundation.
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1996
American Mathematical Society
