Interpolation of uniformly convex Banach spaces
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- by Michael Cwikel and Shlomo Reisner PDF
- Proc. Amer. Math. Soc. 84 (1982), 555-559 Request permission
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.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 555-559
- MSC: Primary 46M35; Secondary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643748-5
- MathSciNet review: 643748