Open Access

Upper Bounds for the Euclidean Operator Radius and Applications

Journal of Inequalities and Applications20082008:472146

DOI: 10.1155/2008/472146

Received: 5 September 2008

Accepted: 3 December 2008

Published: 21 December 2008


The main aim of the present paper is to establish various sharp upper bounds for the Euclidean operator radius of an -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.

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Authors’ Affiliations

Research Group in Mathematical Inequalities & Applications, School of Engineering & Science, Victoria University


© S. S. Dragomir. 2008

This article is published under license to BioMed Central Ltd. 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.