Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Differentiable projections and differentiable semigroups

Author: J. P. Holmes
Journal: Proc. Amer. Math. Soc. 41 (1973), 251-254
MSC: Primary 58C25
MathSciNet review: 0375378
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose $ X$ is a Banach space, $ G$ is a connected open subset of $ X$, and $ p$ is a continuously Fréchet differentiable function from $ G$ into $ G$ satisfying $ p(p(x)) = p(x)$ for each $ x$ in $ G$. We prove that $ p(G)$ is a differentiable submanifold of $ X$ and use this result to show that the maximal subgroup containing an idempotent in a differentiable semigroup is a Lie group.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58C25

Retrieve articles in all journals with MSC: 58C25

Additional Information

PII: S 0002-9939(1973)0375378-1
Keywords: Differentiable manifold, differentiable semigroup
Article copyright: © Copyright 1973 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia