Distance From Projections to Nilpotents

Macdonald, Gordon W.

Canadian journal of mathematics, Tome 47 (1995) no. 4, pp. 841-851

Résumé

The distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k × k matrices with the usual operator norm, is shown to be sec(π/(k:+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k × k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of k × k matrices is .

Détail

DOI : 10.4153/CJM-1995-043-3

Mots-clés : 47A58, 15A99

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