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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 690806, 11 pages
Research Article

Quasi-Jordan Banach Algebras

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455-5, Riyadh 11451, Saudi Arabia

Received 16 November 2013; Accepted 14 January 2014; Published 25 March 2014

Academic Editor: Marco Sabatini

Copyright © 2014 Reem K. Alhefthi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We initiate a study of quasi-Jordan normed algebras. It is demonstrated that any quasi-Jordan Banach algebra with a norm unit can be given an equivalent norm making the algebra isometrically isomorphic to a closed right ideal of a unital split quasi-Jordan Banach algebra; the set of invertible elements may not be open; the spectrum of any element is nonempty, but it may be neither bounded nor closed and hence not compact. Some characterizations of the unbounded spectrum of an element in a split quasi-Jordan Banach algebra with certain examples are given in the end.