Continuous multiplicative mappings on $C(X)$
HTML articles powered by AMS MathViewer
- by Gorazd Lešnjak and Peter Šemrl PDF
- Proc. Amer. Math. Soc. 126 (1998), 127-133 Request permission
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
- Charles Hopkins, Rings with minimal condition for left ideals, Ann. of Math. (2) 40 (1939), 712–730. MR 12, DOI 10.2307/1968951
- Helmut Goldmann and Peter emrl, Multiplicative derivations on $C(X)$, Monatsh. Math. 121 (1996), no. 3, 189–197. MR 1383530, DOI 10.1007/BF01298949
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
- Peter emrl, The functional equation of multiplicative derivation is superstable on standard operator algebras, Integral Equations Operator Theory 18 (1994), no. 1, 118–122. MR 1250762, DOI 10.1007/BF01225216
- Peter emrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), no. 6, 1851–1855. MR 1242104, DOI 10.1090/S0002-9939-1995-1242104-8
- A. Turowicz, Sur les fonctionelles continues et multiplicatives, Ann. Soc. Polon. Math. 20 (1947), 135–156.
Additional Information
- Gorazd Lešnjak
- 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 Šemrl
- Affiliation: Faculty of Mechanical Engineering, University of Maribor, Smetanova ul. 17, 2000 Maribor, P. O. Box 224, Slovenia
- Email: peter.semrl@uni-mb.si
- 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
- © Copyright 1998 American Mathematical Society
- 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