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

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Measures with bounded powers on locally compact abelian groups


Author: G. V. Wood
Journal: Trans. Amer. Math. Soc. 268 (1981), 187-210
MSC: Primary 43A10
MathSciNet review: 628454
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ \mu $ is a measure on a locally compact abelian group with its positive and negative convolution powers bounded in norm by $ K < \tfrac{1} {3}(4\cos (\pi /9) + 1) \sim 1.58626$ , then $ \mu $ has the form $ \mu = \lambda (\cos \theta {\delta _x} + i\,\sin \theta {\delta _{xu}})$ where $ \vert\lambda \vert = 1$ and $ {u^2} = e$. Applications to isomorphism theorems are given. In particular, if $ {G_1}$ and $ {G_2}$ are l.c.a. groups and $ T$ is an isomorphism of $ {L^1}({G_1})$ onto $ {L^1}({G_2})$ with $ \left\Vert T \right\Vert < \tfrac{1} {3}(4\,\cos (\pi /9) + 1)$, then either $ {G_1}$ and $ {G_2}$ are isomorphic, or they both have subgroups of order $ 2$ with isomorphic quotients.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A10

Retrieve articles in all journals with MSC: 43A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0628454-9
PII: S 0002-9947(1981)0628454-9
Keywords: Measures, bounded powers, locally compact abelian groups, algebra, homomorphisms, algebra isomorphisms
Article copyright: © Copyright 1981 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