%0 Journal Article
%T Local uniform convexity and Kadec-Klee type properties in -interpolation spaces I: General Theory
%A Peter G. Dodds
%A Theresa K. Dodds
%A Alexander A. Sedaev
%A Fyodor A. Sukochev
%J Journal of Function Spaces and Applications
%D 2004
%I Hindawi Publishing Corporation
%R 10.1155/2004/678358
%X We present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. Using properties of the K-functional of J.Peetre, our approach is based on a detailed analysis of properties of a Banach couple and properties of a K-interpolation functional which guarantee that a given K-interpolation space is locally uniformly convex, or has a Kadec-Klee property. A central motivation for our study lies in the observation that classical renorming theorems of Kadec and of Davis, Ghoussoub and Lindenstrauss have an interpolation nature. As a partiular by-product of our study, we show that the theorem of Kadec itself, that each separable Banach space admits an equivalent locally uniformly convex norm, follows directly from our approach.
%U http://www.hindawi.com/journals/jfsa/2004/678358/abs/