Weight-Almost Greedy Bases


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We introduce the notion of a weight-almost greedy basis and show that a basis for a real Banach space is w-almost greedy if and only if it is both quasi-greedy and w-democratic. We also introduce the notion of a weight-semi-greedy basis and show that a w-almost greedy basis is w-semi-greedy and that the converse holds if the Banach space has finite cotype.

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S. Dilworth

Department of Mathematics

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Email: dilworth@math.sc.edu
美国, 1523 Greene St., Columbia, SC, 29208

Denka Kutzarova

Department of Mathematics; Institute of Mathematics and Informatics

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Email: denka@math.uiuc.edu
美国, 1409 West Green St., Urbana, IL, 61801; 8 Acad. Georgi Bonchev St., Sofia, 1113

Vladimir Temlyakov

Department of Mathematics; Steklov Mathematical Institute of Russian Academy of Sciences; Faculty of Mechanics and Mathematics

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Email: temlyak@math.sc.edu
美国, 1523 Greene St., Columbia, SC, 29208; ul. Gubkina 8, Moscow, 119991; Moscow, 119991

Ben Wallis

Department of Mathematical Sciences

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Email: benwallis@live.com
美国, DeKalb, IL, 60115-2888

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