Coordinate systems in Banach spaces and lattices via descriptive set theory

Abstract: Using methods of descriptive set theory, we answer several questions from the literature regarding different notions of infinite bases in Banach lattices. In particular, under the assumption of analytic determinacy, every σ-order basis (e_n) for a Banach lattice X=[e_n] is a uniform basis, and every uniform basis is Schauder. Regarding Banach spaces, we consider filter Schauder bases for Banach spaces, i.e., in which the norm convergence of partial sums is replaced by norm convergence along some appropriate filter on ℕ. We show that every filter Schauder basis with respect to an analytic filter is also a filter Schauder basis with respect to a Borel filter. The talk is accessible to a general logic audience. This is joint work with Antonio Aviles, Mitchell Taylor and Pedro Tradacete.

functional analysislogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic