Abstract and Applied Analysis
Volume 2012 (2012), Article ID 386785, 6 pages
http://dx.doi.org/10.1155/2012/386785
Research Article

Bounded Approximate Identities in Ternary Banach Algebras

Madjid Eshaghi Gordji,1,2 Ali Jabbari,3 and Gwang Hui Kim4

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, P.O. Box 35195-363, Semnan, Iran
3Young Researchers Club, Ardabil Branch, Islamic Azad University, P.O. Box 15655-461, Ardabil, Iran
4Department of Mathematics, Kangnam University, Youngin, Gyeonggi 446-702, Republic of Korea

Received 16 November 2011; Accepted 30 December 2011

Academic Editor: Marcia Federson

Copyright © 2012 Madjid Eshaghi Gordji 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.

Abstract

Let A be a ternary Banach algebra. We prove that if A has a left-bounded approximating set, then A has a left-bounded approximate identity. Moreover, we show that if A has bounded left and right approximate identities, then A has a bounded approximate identity. Hence, we prove Altman’s Theorem and Dixon’s Theorem for ternary Banach algebras.