Geodesic
Vector Measures with Values in l∞(Γ) and Interpolation of Banach Lattices
Journal of convex analysis, Tome 25 (2018) no. 1, pp. 75-92
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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.
Classification : 46E30, 47B38, 46B42, 46B70
Mots-clés : Vector measures, integration, interpolation 
@article{JCA_2018_25_1_JCA_2018_25_1_a4,
     author = {E. A. S\'anchez P\'erez and R. Szwedek},
     title = {Vector {Measures} with {Values} in {l\protect\textsuperscript{\ensuremath{\infty}}(\ensuremath{\Gamma})} and {Interpolation} of {Banach} {Lattices}},
     journal = {Journal of convex analysis},
     pages = {75--92},
     year = {2018},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a4/}
}
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E. A. Sánchez Pérez; R. Szwedek. Vector Measures with Values in l∞(Γ) and Interpolation of Banach Lattices. Journal of convex analysis, Tome 25 (2018) no. 1, pp. 75-92. http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a4/