Abstract
Ph.D. (Mathematics)
Our objective in this thesis is to investigate two fundamental questions concerning
Riesz operators de ned on a Banach space. Recall that Riesz operators are generalizations of compact operators in the sense that Riesz operators have the same spectral properties as compact operators. However, they do not possess the same algebraic properties as compact operators. Our rst question that we investigate is: When is a Riesz operator a nite rank operator? This question is motivated from the fact that
if a compact operator de ned on a Banach space has closed range, then it is a nite
rank operator. Also, Ghahramani proved that a compact homomorphism de ned on
a C -algebra is a nite rank operator, see . Martin Mathieu, in his paper, generalized the result of Ghahramani by proving that a weakly compact homomorphism de ned on a C -algebra is a nite rank operator...