Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 472146, 20 pages
Research Article

Upper Bounds for the Euclidean Operator Radius and Applications

S. S. Dragomir

Research Group in Mathematical Inequalities & Applications, School of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia

Received 5 September 2008; Accepted 3 December 2008

Academic Editor: Andrós Rontá

Copyright © 2008 S. S. Dragomir. 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.


The main aim of the present paper is to establish various sharp upper bounds for the Euclidean operator radius of an n-tuple of bounded linear operators on a Hilbert space. The tools used are provided by several generalizations of Bessel inequality due to Boas-Bellman, Bombieri, and the author. Natural applications for the norm and the numerical radius of bounded linear operators on Hilbert spaces are also given.