Interpolation of uniformly convex banach spaces

Michael Cwikel; Shlomo Reisner

doi:10.1090/S0002-9939-1982-0643748-5

Interpolation of uniformly convex banach spaces

Research output: Contribution to journal › Article › peer-review

Abstract

If A₀ and A₁are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces [A₀, A₁]ø are also uniformly convex for 0 < ø < 1. Estimates are given for the moduli of convexity and smoothness of [A₀, A₁]ø in terms of these moduli for A₀ and A₁. In general, up to equivalence of moduli these estimates are best possible.

Original language	English
Pages (from-to)	555-559
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	84
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1982-0643748-5
State	Published - Apr 1982
Externally published	Yes

ASJC Scopus subject areas

Mathematics (all)
Applied Mathematics

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10.1090/S0002-9939-1982-0643748-5

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AB - If A0 and A1are a compatible couple of Banach spaces, one of which is uniformly convex, then the complex interpolation spaces [A0, A1]ø are also uniformly convex for 0 < ø < 1. Estimates are given for the moduli of convexity and smoothness of [A0, A1]ø in terms of these moduli for A0 and A1. In general, up to equivalence of moduli these estimates are best possible.

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Interpolation of uniformly convex banach spaces

Abstract

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