SCIENTIFIC INTERESTS
At the beginning of my career as a research worker I was mainly interested
in Control Theory, under the guidance of Prof. G. Santagati, who was my
supervisor during the preparation of my Thesis. A big portion of
it was devoted to the study of fundamental notions and results in Functional
Analysis. This field of Mathematics resulted very fascinating to me because
of its generality and the possibility of application to other parts of
Mathematical Analysis and other discipline, like Physics. So I started
an accurate study of Functional Analysis and specially of the Geometry
of Banach Spaces, the natural ambit for doing research in modern Mathematical
Analysis. I specialized in studying isomorphic properties of Banach Spaces
and of linear (and nonlinear) operators between two Banach Spaces, sometimes
investigating the chance of application of these theory to other parts
of Mathematical Analysis, like Fixed Point Theory, Theory of Ordinary Differential
Equations and Integral Equations.
Inside Geometry of Banach Spaces I have been
interested, and I still am, in the following topics
1) isomorphic classification of Banach
Spaces, through the study of their isomorphic properties
2) study of linear operators between two
Banach Spaces and their properties that could be useful to distinguish
among different families of spaces
3) study of the spaces of linear operators;
particularly, study of the problem of the existence of continuos projection
from a space of operators onto a proper subspace, that in turn is a space
of operators; such a kind of problem revealed to have a strict connection
with the study of the structure of certain spaces of vector measures and
of Bochner integrable functions
(another of my favourite fields of interest)
4) study of the theory of multilinear mappings
and polynomials in Banach Spaces
5) study of tensor products of Banach Spaces
6) applications of general results to the
Fixed Point Theory and, mainly, to the Theory of Ordinary Differential
Equations and to the Theory of Integral Equations.