On isomorphisms of algebras of smooth functions
HTML articles powered by AMS MathViewer
- by Janez Mrčun PDF
- Proc. Amer. Math. Soc. 133 (2005), 3109-3113 Request permission
Abstract:
We show that for any smooth Hausdorff manifolds $M$ and $N$, which are not necessarily second-countable, paracompact or connected, any isomorphism from the algebra of smooth (real or complex) functions on $N$ to the algebra of smooth functions on $M$ is given by composition with a unique diffeomorphism from $M$ to $N$. An analogous result holds true for isomorphisms of algebras of smooth functions with compact support.References
- Rudolphe Bkouche, Idéaux mous d’un anneau commutatif. Applications aux anneaux de fonctions, C. R. Acad. Sci. Paris 260 (1965), 6496–6498 (French). MR 177002
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
- I. Gelfand and A. Kolmogoroff, On rings of continuous functions on topological spaces, C. R. (Doklady) Acad. Sci. URSS (N. S.) 22 (1939), 11–15.
- J. Mrčun, On spectral representation of coalgebras and Hopf algebroids, Preprint arXiv: math.QA/0208199 (2002).
- Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944
- G. Shilov, Ideals and subrings of the ring of continuous functions, C. R. (Doklady) Acad. Sci. URSS (N. S.) 22 (1939), 7–10.
Additional Information
- Janez Mrčun
- Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
- Email: janez.mrcun@fmf.uni-lj.si
- Received by editor(s): May 18, 2004
- Published electronically: April 8, 2005
- Additional Notes: This work was supported in part by the Slovenian Ministry of Science.
- Communicated by: Jonathan M. Borwein
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 3109-3113
- MSC (2000): Primary 58A05; Secondary 46E25
- DOI: https://doi.org/10.1090/S0002-9939-05-07979-7
- MathSciNet review: 2159792