Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589815 | Journal of Functional Analysis | 2015 | 15 Pages |
Abstract
We introduce and study the notion of an order Schauder basis of a vector lattice E by replacing the norm convergence in the definition of a Schauder basis with the order convergence in E. By a bibasis of a Banach lattice E we mean a sequence which is both a Schauder basis and an order Schauder basis of E . We find necessary and sufficient conditions for a system to be a bibasis, and extend some known theorems on Schauder bases to the setting of bibases. Then we show that the Haar system is a bibasis of LpLp with 1
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Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anna Gumenchuk, Olena Karlova, Mikhail Popov,