Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Continuous multiplicative mappings on $C(X)$


Authors: Gorazd Lesnjak and Peter Semrl
Journal: Proc. Amer. Math. Soc. 126 (1998), 127-133
MSC (1991): Primary 46E25, 46J10
DOI: https://doi.org/10.1090/S0002-9939-98-03967-7
MathSciNet review: 1402871
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ and $Y$ be compact Hausdorff topological spaces, and let $C(X)$ and $C(Y)$ be real Banach algebras of all real-valued continuous functions on $X$ and $Y$, respectively. The general form of continuous multiplicative mappings $\Phi\colon C(X)\to C(Y)$ is given.


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

  • 1. D. G. Bourgin, Multiplicative transformations, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 564-570. MR 12:421b
  • 2. H. Goldmann and P. \v{S}emrl, Multiplicative derivations on $C(X)$, Monatsh. Math. 121 (1996), 189-198. MR 96m:46041
  • 3. A. N. Milgram, Multiplicative semigroups of continuous functions, Duke Math. J. 16 (1949), 377-383. MR 10:612a
  • 4. P. \v{S}emrl, The functional equation of multiplicative derivation is superstable on standard Banach algebras, Integr. Equat. Oper. Th. 18 (1994), 118-122. MR 94k:47055
  • 5. P. \v{S}emrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), 1851-1855. MR 95g:47066
  • 6. A. Turowicz, Sur les fonctionelles continues et multiplicatives, Ann. Soc. Polon. Math. 20 (1947), 135-156.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46E25, 46J10

Retrieve articles in all journals with MSC (1991): 46E25, 46J10


Additional Information

Gorazd Lesnjak
Affiliation: Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova ul. 17, 2000 Maribor, P. O. Box 218, Slovenia
Email: gorazd.lesnjak@uni-mb.si

Peter Semrl
Affiliation: Faculty of Mechanical Engineering, University of Maribor, Smetanova ul. 17, 2000 Maribor, P. O. Box 224, Slovenia
Email: peter.semrl@uni-mb.si

DOI: https://doi.org/10.1090/S0002-9939-98-03967-7
Received by editor(s): April 30, 1996
Additional Notes: This work was supported by the Ministry of Science and Technology of Slovenia
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society