The Thresholding Greedy Algorithm, Greedy Bases, and Duality

Springer Science and Business Media LLC - Tập 19 - Trang 575-597 - 2003
S.J. Dilworth1, N.J. Kalton2, Denka Kutzarova3, V.N. Temlyakov4
1Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
2Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA
3Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria and Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
4Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

Tóm tắt

Some new conditions that arise naturally in the study of the Thresholding Greedy Algorithm are introduced for bases of Banach spaces. We relate these conditions to best n-term approximation and we study their duality theory. In particular, we obtain a complete duality theory for greedy bases.