Document Zbl 0761.16009

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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 41 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

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