Ascent, Essential Ascent, Descent and Essential Descent for a Linear Relation in a Linear Space

Abstract

For a linear relation in a linear space some spectra dened by means of ascent,
essential ascent, descent and essential descent are introduced and studied. We provethat the algebraic ascent, essential ascent, descent and essential descent spectrum of a linear relation in a linear space satisfy the polynomial spectral mapping theorem. As an application of the obtained results we show that the topological ascent, essential ascent, descent and essential descent spectrum verify the polynomial spectral
mapping theorem.