%0 Journal Article
%T Local Uniform Convexity and Kadec-Klee Type Properties in -interpolation spaces II
%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 10.1155/2004/849723
%X We study local uniform convexity and Kadec-Klee type properties in K-interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and) non-commutative Lorentz spaces possess the (so-alled) (DGL)-property originally introduced by Davis, Ghoussoub and Lindenstrauss in the context of renorming order continuous Banach latties. This property is used as a key tool to show that local uniform convexity and certain Kadec-Klee type properties in non-commutative symmetric spaces of measurable operators may be inferred from corresponding properties of the parameter space of the K-interpolation method. Further applications are given to renorming properties of separable symmetric Banach function spaces and their non-commutative counterparts.
%U http://www.hindawi.com/journals/jfsa/2004/849723/abs/