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Weak convergence in metric spaces and theory of concentrated compactness in Banach spaces

Cyril Tintarev, Uppsala University, USA
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:  Delta-convergence 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.  Delta-convergence 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 Delta-limits, 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 Delta-convergence and proved a Delta-compactness theorem four decades ago.

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