Products of commuting nilpotent operators

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Damjana Kokol Bukovsek
Tomaž Košir
Nika Novak
Polona Oblak

Abstract

Matrices that are products of two (or more) commuting square-zero matrices and
matrices that are products of two commuting nilpotent matrices are characterized. Also given are
characterizations of operators on an infinite dimensional Hilbert space that are products of two (or
more) commuting square-zero operators, as well as operators on an infinite-dimensional vector space
that are products of two commuting nilpotent operators.

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