On the Structure of Essentially Semi-Regular Linear Relations

  • Teresa Álvarez
  • Sonia Keskes
  • Maher MnifEmail author


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 \(\lambda \in \mathbb {C}\) in an essentially semi-regular domain.


Essentially semi-regular linear relations Samuel multiplicity Semi-Fredholm linear relation Kato decomposition 

Mathematics Subject Classification

47A06 47A53 47A10 



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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OviedoOviedoSpain
  2. 2.Laboratory of Mathematical Physics, Department of MathematicsUniversity of Sfax, Faculty of Sciences of SfaxSfaxTunisia

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