On reiteration and the behaviour of weak compactness under certain interpolation methods (Q1817897)

This article deals with K- and J-spaces defined by means of polygons. First, we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We show that if just one restriction of the operator \(T\) is weakly compact, then the interpolation operator from a J-space into a K-space also has this property, but in general this is not the case if we consider \(T\) acting between two J-spaces or two K-spaces. For these cases we prove that the interpolated operator is weakly compact provided that all but two restrictions of \(T\) (located in adjacent vertices of the polygon) are weakly compact. We also show by means of examples that these results are best possible.