When unit groups of continuous inverse algebras are regular Lie groups

Studia Mathematica

Volumn 211, Issue 2, 2012, Pages 95-109

  Glöckner, Helge ^a   Neeb, Karl Hermann ^b  

^a UNIVERSITY OF PADERBORN   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Continuous inverse algebra; Evolution; Infinite dimensional Lie group; Initial value problem; Left logarithmic derivative; Locally m convex algebra; Parameter dependence; Product integral; Q algebra; Regular Lie group; Regularity; Waelbroeck algebra

Indexed keywords

EID: 84869175032     PISSN: 00393223     EISSN: 17306337     Source Type: Journal    
DOI: 10.4064/sm211-2-1     Document Type: Article

References (20)

1. W. Bertram, H. Glöckner and K.-H. Neeb, Di-erential calculus over general base-elds and rings, Expo. Math. 22 (2004), 213-282.
2. J. Bochnak and J. Siciak, Analytic functions in topological vector spaces, Studia Math. 39 (1971), 77-112.
3. R. Dahmen, Direct limit constructions in in-nite-dimensional Lie theory, doctoral dissertation, Univ. Paderborn, 2011; http://nbn-resolving.deurn:nbn:de: hbz:466:2-239.
4. H. Glöckner, In-nite-dimensional Lie groups without completeness restrictions, in: Banach Center Publ. 55, Inst. Math., Polish Acad. Sci., Warszawa, 2002, 43-59.
5. H. Glöckner, Lie group structures on quotient groups and universal complexi-cations for in-nite-dimensional Lie groups, J. Funct. Anal. 194 (2002), 347-409.
6. H. Glöckner, Algebras whose groups of units are Lie groups, Studia Math. 153 (2002), 147-177.
7. H. Glöckner, Direct limits of in-nite-dimensional Lie groups, in: Developments and Trends in In-nite-Dimensional Lie Theory, K.-H. Neeb and A. Pianzola (eds.), Progr. Math. 288, Birkhauser, Boston, 2011, 243-280.
8. H. Glöckner, Notes on regularity properties of in-nite-dimensional Lie groups, arXiv: 1208.0715.
9. H. Glöckner, Regularity in Milnor's sense for direct limits of in-nite-dimensional Lie groups, manuscript in preparation.
10. H. Glöckner and K.-H. Neeb, In-nite-Dimensional Lie Groups, Vol. I, book in preparation.
11. M. Herv-e, Analyticity in In-nite-Dimensional Spaces, de Gruyter, Berlin, 1989.
12. J. L. Kelley, General Topology, Springer, 1955.
13. A. Kriegl and P. W. Michor, The Convenient Setting of Global Analysis, Amer. Math. Soc., Providence, RI, 1997.
14. E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952).
15. P. W. Michor, Manifolds of Di-erentiable Mappings, Shiva Publ., Orpington, 1980.
16. J. Milnor, Remarks on in-nite-dimensional Lie groups, in: Relativit-e, groupes et topologie II (Les Houches, 1983), B. S. DeWitt and R. Stora (eds.), North-Holland, Amsterdam, 1984, 1007-1057.
17. K.-H. Neeb, Towards a Lie theory of locally convex groups, Japan. J. Math. 1 (2006), 291-468.
18. Th. Robart, On Milnor's regularity and the path-functor for the class of in-nite dimensional Lie algebras of CBH type, Algebras Groups Geom. 21 (2004), 367-386.
19. Ph. Turpin, Une remarque sur les alg-ebres-A inverse continu, C. R. Acad. Sci. Paris S-er. A-B 270 (1970), A1686-A1689.
20. L. Waelbroeck, Les alg-ebres-A inverse continu, C. R. Acad. Sci. Paris 238 (1954), 640-641.