REPRESENTATION DU SPECTRE DES OPERATEURS DE HILBERTL-SCHMIDT

Abstract

Defined betwen two Hilbert spaces  and  , the Hilbert-Schmidt operators are summarily introduced by almost all of authors. There are defined in the sommability context of the familly double into [0, +∞[ as we can see it in this text. We have proved that in  the final dimension, those operators are confused with the final row operators and they are called compacts. However in the infinite dimension, the sets of three operators are included one another. Concerning their spectrum representation, it depends on their dimension and the fact that the space   is separable or no separable.