Harte, Robin On quasinilpotents in rings. (English) Zbl 0761.16009 Panam. Math. J. 1, No. 1, 10-16 (1991). The present paper is an attempt to characterize in a general associative ring with identity those elements which play the role of “quasinilpotent” elements in a unital complex Banach algebra. Two possible definitions of such “quasinilpotent” elements are regarded. The comparison with results in the case of normed resp. Banach algebras (the author [Invertibility and Singularity for Bounded Linear Operators (Marcel Dekker, Inc., New York and Basel, 1988; Zbl 0636.47001)]) shows that the given definition aren’t yet satisfying. Reviewer: M.Fritzsche (Potsdam) Cited in 42 Documents MSC: 16N40 Nil and nilpotent radicals, sets, ideals, associative rings 46H05 General theory of topological algebras 16U99 Conditions on elements Keywords:quasinilpotent elements; Banach algebras Citations:Zbl 0636.47001 × Cite Format Result Cite Review PDF