Weak convergence in metric spaces and theory of concentrated compactness in Banach spaces
Speaker 
Cyril Tintarev, Uppsala University, USA


When 
Jan 14, 2016
from 04:00 PM to 05:00 PM 
Where  LH006 
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Abstract: Deltaconvergence is a mode of convergence in metric spaces, which is weaker than usual convergence. It coincides with weak convergence in Hilbert spaces, but not necessarily so in Banach spaces. Deltaconvergence appears in the fixed point theory, and, recently, in analysis of concentration: a bounded sequence in a Banach space is an asymptotic sum of blowups that are defined as deflating Deltalimits, rather than weak limits, of the sequence. In practice, harmonic analysis supplies Besov and TL spaces (including Sobolev spaces) with an equivalent norm for which Delta and weak convergence coincide. This talk is dedicated to the memory of T.C. Lim, who introduced Deltaconvergence and proved a Deltacompactness theorem four decades ago.