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Published online by Cambridge University Press: 05 September 2025
We investigate the notion of ideal (equivalently: filter) Schauder basis of a Banach space. We do so by providing bunch of new examples of such bases that are not the standard ones, especially within classical Banach spaces ($\ell _p$,
$c_0$, and James’ space). Those examples lead to distinguishing and characterizing ideals (equivalently: filters) in terms of Schauder bases. We investigate the relationship between possibly basic sequences and ideals (equivalently: filters) on the set of natural numbers.