Sur la minimisation de la normed’un opérateur élémentaire et applications

Abstract

In this thesis the general problem is minimizing the C_{∞} norm of suitable affine mappings from B(H) to C_{∞} and B(H) → B(H).Using convex and differential analyses (Gateaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained characterize global minima in term of ( Banach space) orthogonality, and constitute an interesting combination of infinite-dimensional differentiable analysis, operator theory and duality . Note that the results obtained generalize some results in the literature concerning operator which are orthogonal to the range of derivation