Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces
The authors of the paper under review for a linear relation introduce and study the notions of ascent, descent, nullity, and defect. It is shown that the results of \textit{A.\,E.\thinspace Taylor} [Math.\ Ann.\ 163, 18--49 (1966; Zbl 0138.07602)] and \textit{M.\,A.\thinspace Kaashoek} [Math.\ Ann.\ 172, 105--115 (1967; Zbl 0152.33803)] for linear operators are also valid in the case of linear relations that do not have nontrivial singular chains. Examples are given that in the case when there are such chains, the corresponding results are not valid.
scientific article; zbMATH DE number 5151580
scientific article