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

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

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Title: Essential g-ascent and g-descent of a closed linear relation in Hilbert spaces
Author: Garbouj, Zied; Skhiri, Haïkel
Abstract: 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.
URI: http://hdl.handle.net/10662/8903
Date: 2017


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