English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

For Schauder bases, Dilworth et al. introduced and characterized thepartially greedy property, which is strictly weaker than the (almost) greedyproperty. Later, Berasategui et al. defined and studied the strong partiallygreedy property for general bases. Let $\mathbf n$ be any strictly increasingsequence of positive integers. In this paper, we define the strong partiallygreedy property with respect to $\mathbf n$, called the ($\mathbf n$, strongpartially greedy) property. We give characterizations of this new property,study relations among ($\mathbf n$, strong partially greedy) properties fordifferent sequences $\mathbf n$, establish Lebesgue-type inequalities for the($\mathbf n$, strong partially greedy) parameter, investigate ($\mathbf n$,strong partially greedy) bases with gaps, and weighted ($\mathbf n$, strongpartially greedy) bases, to name a few. Furthermore, we introduce the ($\mathbfn$, almost greedy) property and equate the property to a strengthening of the($\mathbf n$, strong partially greedy) property. This paper can be viewed bothas a survey of recent results regarding strong partially greedy bases and as anatural and nontrivial extension of these results to an arbitrary sequenceinstead of $\mathbb{N}$.

Strong Partially Greedy Bases with Respect to an Arbitrary Sequence