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  • Research Article
  • Open Access

Upper Bounds for the Euclidean Operator Radius and Applications

Journal of Inequalities and Applications20082008:472146

  • Received: 5 September 2008
  • Accepted: 3 December 2008
  • Published:


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.


  • Full Article
  • Publisher Note
  • Operator Radius
  • Euclidean Operator

Publisher note

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Authors’ Affiliations

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


© 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.