Interpolation methods to estimate eigenvalue distribution of some integral operators.
Interpolation of Operator Ideals with an Application to Eigenvalue Distribution Problems.
Interpolation of real method spaces via some ideals of operators
Certain operator ideals are used to study interpolation of operators between spaces generated by the real method. Using orbital equivalence a new reiteration formula is proved for certain real interpolation spaces generated by ordered pairs of Banach lattices of the form . As an application we extend Ovchinnikov’s interpolation theorem from the context of classical Lions-Peetre spaces to a larger class of real interpolation spaces. A description of certain abstract J-method spaces is also presented....
Interpolation of semigroups and integrated semigroups.
Interpolation of Spectral Operators.
Interpolation of the essential spectrum and the essential norm
The behavior of the essential spectrum and the essential norm under (complex/real) interpolation is investigated. We extend an example of Albrecht and Müller for the spectrum by showing that in complex interpolation the essential spectrum of an interpolated operator is also in general a discontinuous map of the parameter θ. We discuss the logarithmic convexity (up to a multiplicative constant) of the essential norm under real interpolation, and show that this holds provided certain compact approximation...
Interpolation of the measure of non-compactness between quasi-Banach spaces.
We study the behavior of the ball measure of non-compactness under several interpolation methods. First we deal with methods that interpolate couples of spaces, and then we proceed to extend the results to methods that interpolate finite families of spaces. We will need an approximation hypothesis on the target family of spaces.
Interpolation of the measure of non-compactness by the real method
We investigate the behaviour of the measure of non-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.
Interpolation properties associated with the second order abstract Cauchy problem.
Interpolation spaces with function parameter and measures of non-compactness.
Interpolation theorem for the p-harmonic transform
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...
Interpolation theorems for operators relatively bounded by differential-type transformations.
Interpolation theory and measures related to operator ideals
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.
Interpolationseigenschaften des Spektrums linearer Operatoren auf Lp-Räumen.
Interpolationsfunktoren, Folgenideale und Operatorenideale
Intersection of moving convex sets in a normed space.
Intersection properties of balls in spaces of compact operators
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...
Intertwining methods in the problem of inverse scattering
Intertwining Multiplication Operators on Function Spaces
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.
Intertwining of Markov semi-groups, some examples