Affiliation:
1. Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Laboratory of Mathematical Physics, Sfax, Tunisia
Abstract
In the case of linear operator the property P(B, k) was introduced by
M.A. Kaashoek. In this paper, we characterize the essentially semi regular
linear relation in terms of the property P(B, k). After that and as an
application of this result we give some connection between essentially semi
regular and semi regular linear relations. Further, we will give some
supplementary conditions on essentially semi regular linear relation to be
semi Fredholm. Then, we analyze the stability of the class of essentially
semi regular linear relations under small perturbations and Riesz operators.
Finally, we study some properties of the essentially semi regular spectrum
of a linear relation and we establish a spectral mapping theorem.
Publisher
National Library of Serbia