A Banach space with L-orthogonal sequences but without L-orthogonal elements
Abstract
We prove that the existence of Banach spaces with L-orthogonal sequences but without L-orthogonal elements is independent of the standard foundation of Mathematics, ZFC. This provides a definitive answer to [Question~1.1]AvilesMartinezRueda. Generalizing classical Q-point ultrafilters, we introduce the notion of Q-measures and provide several results generalizing former theorems by Miller Miller and Bartoszynski Bartoszynski for Q-point ultrafilters.
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