Interpolation properties associated with the second order abstract Cauchy problem.
We establish an interpolation theorem for a class of nonlinear operators in the Lebesgue spaces arising naturally in the study of elliptic PDEs. The prototype of those PDEs is the second order p-harmonic equation . In this example the p-harmonic transform is essentially inverse to . To every vector field our operator assigns the gradient of the solution, . The core of the matter is that we go beyond the natural domain of definition of this operator. Because of nonlinearity our arguments...
Given any operator ideal , there are two natural functionals , that one can use to show the deviation of the operator to the closed surjective hull of and to the closed injective hull of , respectively. We describe the behaviour under interpolation of and . The results are part of joint works with A. Martínez, A. Manzano and P. Fernández-Martínez.
We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space to a space has the 3.2 intersection property if and only if and have the 3.2 intersection property and...
Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.