Distance from Idempotents to Nilpotents

MacDonald, Gordon W.

Canadian journal of mathematics, Tome 59 (2007) no. 3, pp. 638-657

Résumé

We give bounds on the distance from a non-zero idempotent to the set of nilpotents in the set of $n\,\times \,n$ matrices in terms of the norm of the idempotent. We construct explicit idempotents and nilpotents which achieve these distances, and determine exact distances in some special cases.

Détail

DOI : 10.4153/CJM-2007-027-x

Mots-clés : 47A15, 47D03, 15A30, operator, matrix, nilpotent, idempotent, projection

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