Geodesic
Normed Lie Algebras
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 580-591

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we attempt to define the notion of normed Lie algebra by endowing the corresponding algebraic concept with topologicalmetric properties. More precisely, we define normed Lie algebras as being normed spaces possessing a Lie product, the latter satisfying a compatibility relation. It turns out that any normed algebra, in particular the algebra of continuous linear operators on a normed space, is a normed Lie algebra in the sense denned below, with the usual Lie product given by the additive commutator.It seems that some algebraic features have within the framework of normed Lie algebras the natural topological extensions. We mention, for instance, the convergence of the well-known Campbell-Hausdorff formula. Let us also mention the occurence of a variant of the Kleinecke-Sirokov theorem, obtained via universal enveloping algebra, which might be unknown in this context. 
Vasilescu, F.-H. Normed Lie Algebras. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 580-591. doi: 10.4153/CJM-1972-052-7
@article{10_4153_CJM_1972_052_7,
     author = {Vasilescu, F.-H.},
     title = {Normed {Lie} {Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {580--591},
     year = {1972},
     volume = {24},
     number = {4},
     doi = {10.4153/CJM-1972-052-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-052-7/}
}
TY  - JOUR
AU  - Vasilescu, F.-H.
TI  - Normed Lie Algebras
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 580
EP  - 591
VL  - 24
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-052-7/
DO  - 10.4153/CJM-1972-052-7
ID  - 10_4153_CJM_1972_052_7
ER  - 
%0 Journal Article
%A Vasilescu, F.-H.
%T Normed Lie Algebras
%J Canadian journal of mathematics
%D 1972
%P 580-591
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-052-7/
%R 10.4153/CJM-1972-052-7
%F 10_4153_CJM_1972_052_7

[1] 1. Bourbaki, N., Groupes et algèbres de Lie, Eléments de Mathématiques (Hermann, Paris, 1960). Google Scholar

[2] 2. Halmos, P. R., Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887–933. Google Scholar

[3] 3. Jacobson, N., Lie algebras (Interscience, New York, 1962). Google Scholar

[4] 4. Putnam, C. R., Commutation properties of Hilbert space operators and related topics (Springer-Verlag, New York, 1967). Google Scholar

[5] 5. Putnam, C. R., Séminaire “Sophys Lie”, 1954-1955. Théorie des Algèbres de Lie; Topologie des groupes de Lie (Secrétariat Mathématique, Paris, 1955). Google Scholar

[6] 6. Serre, J. P., Lie algebras and Lie groups, Lectures given at Harvard University (Benjamin, New York, Amsterdam, 1965). Google Scholar

[7] 7. Stampfli, J. G., The norm of a derivation, Pacific J. Math. 38 (1970), 737–747. Google Scholar

[8] 8. Sabac, M., Une géneralisation du théorème de Lie, Bull. Sci. Math. 95 (1971), 53–57. Google Scholar

[9] 9. Vasilescu, F.-H., On Lie1 s theorem in operator algebras, Trans. Amer. Math. Soc. (to appear). Google Scholar

Cité par Sources :