Propriétés des opérateurs de dérivation et théorème de fugled-putnam

Abstract

The second chapter deals with the Jordan form of the generalized derivation operator’s (X)=AXXB and the elementary derivation operator (X)=AXB-CXD. In the third chapter we consider the pairs of operators (A,B) such as AT=TB implies T=T for any T∈C₁(H), i.e the pairs that satisfy Fugled –Putnam’s theorem in C₁(H) (C₁(H) is an ideal of ℒ(H)), that we call generalized P-symmetric. We give some basic properties for this class, and we focus, as well, in this chapter on the study of the pairs’ class of elementary P-symmetric operators ( (A,B) is elementary P-symmetric if BTA=T⇒ T =T. In the last chapter we present a global study on the orthogonality of the image to the kernel of the intern derivation (X)=AX-XA and of the finite operators.