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

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


Locally $ B\sp{\ast} $-equivalent algebras. II

Author: Bruce A. Barnes
Journal: Trans. Amer. Math. Soc. 176 (1973), 297-303
MSC: Primary 46K05
MathSciNet review: 0320762
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let A be a locally $ {B^\ast}$-equivalent Banach $ ^\ast$-algebra. Then A possesses a unique norm $ \vert \cdot \vert$ with the property that $ \vert{a^\ast}a\vert = \vert a{\vert^2}$ for all $ a \in A$. Let B be the $ {B^\ast}$-algebra which is the completion of A in the norm $ \vert \cdot \vert$. In this paper it is shown that there exists a closed $ {B^\ast}$-equivalent $ ^\ast$-ideal of A which contains the maximal GCR ideal of B. In particular, when B is a GCR algebra, then $ A = B$.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46K05

Retrieve articles in all journals with MSC: 46K05

Additional Information

PII: S 0002-9947(1973)0320762-X
Article copyright: © Copyright 1973 American Mathematical Society