Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A new proof on the characterization of vanishing subalgebras of group algebras

Author: F. Ghahramani
Journal: Proc. Amer. Math. Soc. 142 (2014), 617-621
MSC (2010): Primary 43A20
Published electronically: November 13, 2013
MathSciNet review: 3134002
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a new proof to a result due to T. Shimizu stating that for a locally compact group $ G$ and the associated group algebra $ L^{1}(G)$, if $ S$ is a measurable subset of $ G$, then a necessary and sufficient condition for the subspace of all functions in $ L^{1}(G)$ that vanish almost everywhere off $ S$ to be an algebra is that $ S$ is equal to a subsemigroup of $ G$, locally almost everywhere. Our proof bypasses a deep result of A. Ionescu Tulcea and C. Ionescu Tulcea, used in Shimizu's proof, and is for the most part functional analytic.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 43A20

Retrieve articles in all journals with MSC (2010): 43A20

Additional Information

F. Ghahramani
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada

Keywords: Arens product, contractive projections, group algebra, semigroup, vanishing algebra
Received by editor(s): July 20, 2011
Received by editor(s) in revised form: March 30, 2012
Published electronically: November 13, 2013
Additional Notes: The author’s research was supported by NSERC Grant 36640-07
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.