Hello,
The next Banach spaces webinar is on Friday May 14 at 9AM Central time. Please join us at
https://unt.zoom.us/j/83807914306
Speaker: Harrison Gaebler, University of Kansas Title: Asymptotic Geometry of Banach Spaces that have a Well-Behaved Riemann Integral
Abstract: Banach spaces for which Riemann integrability implies Lebesgue almost everywhere continuity are said to have the Property of Lebesgue, or to be ``PL-spaces." It is an open problem to derive a full characterization of PL-spaces. In this talk, I will first give a brief overview of Riemann and Darboux integrability for Banach-valued functions, and I will then introduce the Property of Lebesgue with some relevant examples. I will next show how the Property of Lebesgue is connected to the asymptotic geometry (both global and local) of the underlying Banach space, and I will present three new results in this direction that are to appear later this year in Real Analysis Exchange. Finally, I will discuss two possibilities for future research on characterizing PL-spaces, and a connection between the Property of Lebesgue and the distortion of the unit sphere as well.
For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach