Seminar on Banach and Metric Space Geometry

Date: February 3, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Przemyslaw Wojtaszczyk, University of Warsaw

Title: Conditionality constants of quasi-greedy bases

Abstract: For a conditional quasi-greedy basis B in a Banach space the associated conditionality constants km[B] verify the estimate km[B]=O(logm). Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied whether this bound can be improved when we consider quasi-greedy bases in some special class of spaces. It is known that every quasi-greedy basis in a superreflexive Banach space verifies km[B]=(logm)1-ϵ for some 0<ϵ<1, and this is optimal. Our first goal in this paper will be to fill the gap in between the general case and the superreflexive case and investigate the growth of the conditionality constants in non-superreflexive spaces. Roughly speaking, the moral will be that we can guarantee optimal bounds only for quasi-greedy bases in superreflexive spaces. Joint work with F.Albiac and Jose L. Ansorena.