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Interpolation of uniformly convex Banach spaces


Authors: Michael Cwikel and Shlomo Reisner
Journal: Proc. Amer. Math. Soc. 84 (1982), 555-559
MSC: Primary 46M35; Secondary 46B20
MathSciNet review: 643748
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Abstract: If $ {A_0}$ and $ {A_1}$ are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces $ {[{A_0},{A_1}]_\theta }$ are also uniformly convex for $ 0 < \theta < 1$. Estimates are given for the moduli of convexity and smoothness of $ {[{A_0},{A_1}]_\theta }$ in terms of these moduli for $ {A_0}$ and $ {A_1}$. In general, up to equivalence of moduli these estimates are best possible.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0643748-5
Article copyright: © Copyright 1982 American Mathematical Society