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)


Completion of norms for $ C(X,\,Q)$

Author: Edith H. Luchins
Journal: Proc. Amer. Math. Soc. 28 (1971), 478-480
MSC: Primary 46.55
MathSciNet review: 0273412
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ C(X,Q)$ denote the algebra of all continuous quaternion-valued functions vanishing at infinity on a locally compact Hausdorff space $ X$. Under the natural norm (the sup norm) and under the spectral radius norm, $ r(f)$, which is equivalent to the sup norm, $ C(X,Q)$ is a Banach algebra. Let $ \delta (f)$ be any multiplicative norm for $ C(X,Q)$; i.e., one under which it is a normed algebra. It is shown that $ \delta (f)$, whether or not it is complete, majorizes the natural norm and $ r(f)$. Under certain conditions on the radical of the completion of $ \delta (f),\delta (f)$ is equivalent to the natural norm and $ r(f)$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.55

Retrieve articles in all journals with MSC: 46.55

Additional Information

PII: S 0002-9939(1971)0273412-9
Keywords: Real Banach algebra, quaternion-valued continuous functions, sup, minimal, incomplete and equivalent norms, radical, semisimple, strictly semisimple
Article copyright: © Copyright 1971 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