ELA, Volume 16, pp. 237-247, September 2007, abstract.

Products of Commuting Nilpotent Operators

Damjana Kokol Bukovsek, Tomaz Kosir, Nika Novak, and
Polona Oblak

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.