========================================= 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> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Michael Cwikel <mcwikel@math.technion.ac.il>