Interpolation of Uniformly Convex Banach Spaces
Copyright policy )Interpolation of Uniformly Convex Banach Spaces
If A 0 {A_0} and A 1 {A_1} are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces [ A 0 , A 1 ] θ {[{A_0},{A_1}]_\theta } are also uniformly convex for 0 > θ > 1 0 > \theta > 1 . Estimates are given for the moduli of convexity and smoothness of [ A 0 , A 1 ] θ {[{A_0},{A_1}]_\theta } in terms of these moduli for A 0 {A_0} and A 1 {A_1} . In general, up to equivalence of moduli these estimates are best possible.
Geometry and structure of normed linear spaces, complex interpolation spaces, compatible couples of Banach spaces, Abstract interpolation of topological vector spaces, uniform convexity, moduli of convexity and smoothness
Geometry and structure of normed linear spaces, complex interpolation spaces, compatible couples of Banach spaces, Abstract interpolation of topological vector spaces, uniform convexity, moduli of convexity and smoothness
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