Abstract
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.
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