When unit groups of continuous inverse algebras are regular Lie groups

Volume 211 / 2012

Helge Glöckner, Karl-Hermann Neeb Studia Mathematica 211 (2012), 95-109 MSC: Primary 22E65; Secondary 34G10, 46G20, 46H05, 58B10. DOI: 10.4064/sm211-2-1

Abstract

It is a basic fact in infinite-dimensional Lie theory that the unit group $A^\times $ of a continuous inverse algebra $A$ is a Lie group. We describe criteria ensuring that the Lie group $A^\times $ is regular in Milnor's sense. Notably, $A^\times $ is regular if $A$ is Mackey-complete and locally m-convex.

Authors

  • Helge GlöcknerUniversität Paderborn
    Institut für Mathematik
    Warburger Str. 100
    33098 Paderborn, Germany
    e-mail
  • Karl-Hermann NeebFAU Erlangen-Nürnberg
    Department Mathematik
    Cauerstr. 11
    91058 Erlangen, Germany
    e-mail

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