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Journal of Function Spaces and Applications
Volume 2012, Article ID 713534, 19 pages
http://dx.doi.org/10.1155/2012/713534
Research Article

Best Constants between Equivalent Norms in Lorentz Sequence Spaces

1Department of Mathematics, Karlstad University, 65188 Karlstad, Sweden
2Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020 396 Bucharest, Romania
3Department of Mathematics, Luleå University of Technology, 97 187 Luleå, Sweden

Received 19 March 2010; Accepted 24 May 2010

Academic Editor: Nicolae Popa

Copyright © 2012 S. Barza 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

We find the best constants in inequalities relating the standard norm, the dual norm, and the norm x(p,s):=inf{kx(k)p,s}, where the infimum is taken over all finite representations x=kx(k) in the classical Lorentz sequence spaces. A crucial point in this analysis is the concept of level sequence, which we introduce and discuss. As an application, we derive the best constant in the triangle inequality for such spaces.