Essential g-ascent and g-descent of a closed linear relation in Hilbert spaces

We define and discuss for a closed linear relation in a Hilbert space the notions of essential g-ascent (resp. g-descent) and g-ascent (resp. g-descent) spectrums. We improve in the Hilbert space case some results given by E. Chafai in a Banach space [Acta Mathematica Sinica, 34 B, 1212-1224, 2014] and several results related to the ascent (resp. essential ascent) spectrum for a bounded linear operator on a Banach space [Studia Math, 187, 59-73, 2008] are extended to closed linear relations on Hilbert spaces. We prove also a decomposition theorem for closed linear relations with finite essential g-ascent or g-descent.This work is supported by the Higher Education And Scientific Research In Tunisia, UR11ES52: Analyse, Géométrie et ApplicationspeerReviewe