Cobos Díaz, FernandoFernández-Cabrera Marín, Luz MaríaKühn, ThomasUllrich, Tino2023-06-202023-06-2020090022-123610.1016/j.jfa.2008.12.013https://hdl.handle.net/20.500.14352/49863We investigate the limit class of interpolation spaces that comes up by the choice θ = 0 in the definition of the real method. These spaces arise naturally interpolating by the J -method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ = 1. We also study the behavior of compact operators under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators.engjournal articlehttps//doi.org/10.1016/j.jfa.2008.12.013http://www.sciencedirect.com/science/article/pii/S0022123608005417restricted access517Extreme interpolation spacesReal interpolationJ -functionalK-functionalInterpolation methodsCompact-OperatorsBanach-SpacesPolygonsExtrapolationReiterationDualityMathematics associated to polygonsCompact operatorsLorentz–Zygmund function spacesSpaces of operatorsAnálisis matemático1202 Análisis y Análisis Funcional