Analytic Convexity and Complex Interpolation.
Antonio Bernal, Joan Cerda (1992)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Analytic Convexity and Complex Interpolation.
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The behavior of compactness under real interpolation real is discussed. Classical results due to Krasnoselskii, Lions-Peetre, Persson, and Hayakawa are described, as well as others obtained very recently by Edmunds, Potter, Fernández, and the author.
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We study those compatible couples of Banach spaces for which the complex method interpolation spaces are also described by the K-method of interpolation. As an application we present counter-examples to Cwikel's conjecture that all interpolation spaces of a Banach couple are described by the K-method whenever all complex interpolation spaces have this property.