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Journal of Convex Analysis 25 (2018), No. 1, 075--092
Copyright Heldermann Verlag 2018

Vector Measures with Values in l(Γ) and Interpolation of Banach Lattices

Enrique A. Sánchez Pérez
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de València, Camino de Vera s/n, 46022 València, Spain

Radoslaw Szwedek
Faculty of Mathematics and Computer Science, Adam Mickiewicz University in Poznan, Umultowska 87, 61-614 Poznan, Poland

An explicit construction for the representation of the Calderón interpolation of spaces of vector measure integrable functions is given as well as for the representation of the real interpolation of these spaces using the K-functional. In order to do this, we introduce a technique based on interpolation of function valued matrices. For the real interpolation, we develop a vector-valued version of the K-functional having values in l-spaces, providing in this way a new procedure for the study of the interpolation of general Banach lattices.

Keywords: Vector measures, integration, interpolation.

MSC: 46E30; 47B38, 46B42, 46B70

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