The thematic system and axes of my research are divided between the bounded operators theory on Banach spaces, and the spectral theory in the Banach algebras. My research contributions are focused on the following subjects:
- Linear preservers problem: It consists of characterizing all linear, or additive, transformations on algebras that leave invariant certain subsets, functions, or relations.
- Perturbation classes problem: The aim is to completely determine the perturbations class, or the commuting perturbations class, of certain subsets of bounded operators or of certain parts of spectrum.
- Non-Linear preservers problem: It is the question to find the general structure of all maps defined on a Banach algebra, or the bounded linear operators algebra, that preserve the difference or the product of certain subsets, functions, or relations.