LAUSR

The Samuel multiplicity and the structure of essentially semi-regular linear relations on a Banach space are considered. First, we give some results concerning Samuel multiplicity for essentially semi-regular linear relations. Second, we study the structure of essentially semi-regular linear relations on an infinite dimensional complex Banach space. Finally, as an application, we get the structure of semi-Fredholm linear relations and we characterize a semi-Fredholm point $$\lambda \in \mathbb {C}$$λ∈C in an essentially semi-regular domain.