2025/04/07 by Kevin Beanland, Beanland, Kevin, Hùng Việt Chu +5
Mathematics · Computer Science · #Advanced Banach Space Theory #Optimization and Variational Analysis #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.2504.05533
For two countable ordinals α and β, a basis of a Banach space X is said to be (α, β)-quasi-greedy if it is 1) quasi-greedy, 2) Sα-unconditional but not Sα+1-unconditional, and 3) Sβ-democratic but not Sβ+1-democratic. If α or β is replaced with ∞, then the basis is required to be unconditonal or democratic, respectively. Previous work constructed a (0,0)-quasi-greedy basis, an (α, ∞)-quasi-greedy basis, and an (∞, α)-quasi-greedy basis. In this paper, we construct (α, β)-quasi-greedy bases for β≤ α+1 (except the already solved case α= β= 0).