Non-equivalent greedy and almost greedy bases in ℓp. Issue 1 (2006)

• Record Type: Journal Article
• Authors: Dilworth Dilworth, Stephen J. Stephen J.; Hoffmann Hoffmann, Mark Mark; Kutzarova Kutzarova, Denka N. Denka N.
• Other Names: Kalton Kalton Nigel Nigel Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 4:Issue 1(2006)
• Page Start: 25
• Page End: 42
• Publication Date: 2006
• Subjects: Greedy bases -- Haar system -- Lp spaces; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2006/368648
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : For 1 < p < ∞ and p ≠ 2 we construct a family of mutually non-equivalent greedy bases in ℓ p 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 L p and H 1 . Moreover, the technique used in the proof adapts to the setting of almost greedy bases where similar results are obtained.