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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.
We give an equivalent expression for the K-functional associated to the pair of operator spaces (R,C) formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair (Mₙ(R),Mₙ(C)) (uniformly over n). More generally, the same result is valid when Mₙ (or B(ℓ₂)) is replaced by any semi-finite von Neumann algebra. We prove a version of the non-commutative Khintchine inequalities (originally due to Lust-Piquard) that is valid for the Lorentz spaces...
We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for spaces and the recent method of Cobos-Peetre.
We describe the real interpolation spaces between given Marcinkiewicz spaces that have fundamental functions of the form t1/q (ln (e/t)a with the same exponent q. The spaces thus obtained are used for the proof of optimal interpolation theorem from [7], concerning spaces L∞,a,E.
We find necessary and sufficient conditions under which the norms of the interpolation spaces and are equivalent on N, where N is the kernel of a nonzero functional ψ ∈ (X₀ ∩ X₁)* and is the normed space N with the norm inherited from (i = 0,1). Our proof is based on reducing the problem to its partial case studied by Ivanov and Kalton, where ψ is bounded on one of the endpoint spaces. As an application we completely resolve the problem of when the range of the operator (S denotes the...
We prove a reiteration theorem for interpolationmethods defined by means of polygons, and a Wolff theorem for the case when the polygon has 3 or 4 vertices. In particular, we establish a Wolff theorem for Fernandez' spaces, which settles a problem left over in [5].
This note deals with interpolation methods defined by means of polygons. We show necessary and sufficient conditions for compactness of operators acting from a J-space into a K-space.
We study interpolation of bilinear operators by the polygons methods. We prove an interpolation theorem of type into spaces, and show the optimality of the precedings results.
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