BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christian Rosendal (University of Maryland) DTSTART:20260226T190000Z DTEND:20260226T200000Z DTSTAMP:20260423T035936Z UID:OLS/205 DESCRIPTION:Title: Co ordinate systems in Banach spaces and lattices via descriptive set theory< /a>\nby Christian Rosendal (University of Maryland) as part of Online logi c seminar\n\n\nAbstract\nUsing methods of descriptive set theory\, we answ er several questions from the literature regarding different notions of in finite bases in Banach lattices. In particular\, under the assumption of a nalytic 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 Ba nach spaces\, we consider filter Schauder bases for Banach spaces\, i.e.\, in which the norm convergence of partial sums is replaced by norm converg ence along some appropriate filter on ℕ. We show that every filter Schau der basis with respect to an analytic filter is also a filter Schauder bas is with respect to a Borel filter. The talk is accessible to a general log ic audience. This is joint work with Antonio Aviles\, Mitchell Taylor and Pedro Tradacete.\n LOCATION:https://researchseminars.org/talk/OLS/205/ END:VEVENT END:VCALENDAR