Antón Martínez

On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals

We improve the known results on interpolation of strictly singular operators and strictly co-singular operators in several directions. Applications are given to embeddings between symmetric spaces.

Extreme estimates for interpolated operators by the real method

The paper establishes estimates for ideal measures of operators interpolated by the real method in terms of the measures of their restrictions to a sequence of spaces modelled on the intersection. It also shows that the estimates are optimal.

On duality between K - and J -spaces

We study the relationship between the dual of the #C-space defined by means of a polygon and the /-space generated by the dual N-tuple. The results complete the research started in [4]. Special attention is paid to the case when the N-tuple is formed by Banach lattices

Measure of non-compactness and interpolation methods associated to polygons

We establish an estimate for the measure of non-compactness of an interpolated operator acting from a J-space into a K-space. Our result refers to general Banach N-tuples. We also derive estimates for entropy numbers if some of the N-tuples reduce to a single Banach space.

Measure of Non-compactness of Operators Interpolated by Limiting Real Methods

We establish formulae for the measure of non-compactness of operators interpolated by limiting methods that come up by the choice θ = 0 and θ = 1 in the definition of the real method.

Some Interpolation Results that are the Exclusive Property of Compact Operators

We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J -functionals of interpolation theory.