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Technion
 
Analysis seminar
 
Speaker: Eliran Avni (Technion)
 
Title:   Topics in interpolation spaces.
 
Date: Thursday, February 23 at 2:30 p.m.
 
Place: Amado 919.
 
Cookies: 10 minutes before the talk
 
Abstract:
 
In this lecture we address some questions in interpolation spaces.
 
The first question relates to the notion of Calderon couples (also known as
C-couples, K-adequate couples, K-monotone couples and Calderon-Mityagin
couples). These are those couples of Banach spaces for which there is a
relatively simple description of all their interpolation spaces via the
Peetre K-functional.
 
We ask whether the p-convexified couple (X_0^(p),X_1^(p)) is a Calderon
couple under the assumption that (X_0,X_1) is a Calderon couple of Banach
lattices on some measure space.
 
We find that the answer is affirmative whenever certain "mild" additional
conditions are imposed.
 
If time permits we will also discuss a second question which relates to
Calderon's complex interpolation method. More precisely, we will consider
the so-called "periodic" complex interpolation method, studied by Peetre.
(These also correspond to the spaces obtained by Calderon's construction
using Banach space valued analytic functions, but defined on an annulus
instead of the strip used by Calderon.)
 
Cwikel showed that, using functions with a given period i\lambda in the
complex method mechanism, one obtains the same interpolation spaces as in
the original version of the complex method, up to equivalence of norms. He
also showed that one of the constants of this equivalence will, in some
cases, "blow up" as \lambda tends to zero.
 
We will show that the equivalence constants tend to 1 as \lambda tends to
infinity. Intuitively, this means that when applying the complex method, it
makes only a very small difference if one restricts oneself to periodic
functions, provided that the period is very large (or the corresponding
annulus is very thin).
 
Seminar webpage:  <http://www.technion.ac.il/~tamarzr/analysis.html>
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Michael Cwikel   <mcwikel@math.technion.ac.il>