Local Uniform Convexity and Kadec‐Klee Type Properties in K‐interpolation spaces II | Zendy

Peter G. Dodds | Zendy; Theresa K.-Y. Dodds | Zendy; Alexander A. Sedaev | Zendy; Fedor Sukochev | Zendy

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Local Uniform Convexity and Kadec‐Klee Type Properties in K‐interpolation spaces II

Author(s) -

Peter G. Dodds,

Theresa K.-Y. Dodds,

Alexander A. Sedaev,

Fedor Sukochev

Publication year - 2004

Publication title -

journal of function spaces

Language(s) - English

Resource type - Journals

eISSN - 2314-8896

pISSN - 2314-8888

DOI - 10.1155/2004/849723

Subject(s) - mathematics , convexity , type (biology) , interpolation (computer graphics) , combinatorics , pure mathematics , artificial intelligence , computer science , motion (physics) , ecology , financial economics , economics , biology

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

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