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Journal of Function Spaces and Applications
Volume 4 (2006), Issue 1, Pages 25-42
http://dx.doi.org/10.1155/2006/368648

Non-equivalent greedy and almost greedy bases in lp

1Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
2Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
3Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria
4Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

Received 1 November 2004

Academic Editor: Nigel Kalton

Copyright © 2006 Hindawi Publishing Corporation. 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

For 1 < p < 8 and p ? 2 we construct a family of mutually non-equivalent greedy bases in lp having the cardinality of the continuum. In fact, no basis from this family is equivalent to a rearranged subsequence of any other basis thereof. We are able to extend this statement to the spaces Lp and H1. Moreover, the technique used in the proof adapts to the setting of almost greedy bases where similar results are obtained.