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Sums and products of quasi-nilpotent operators. (English) Zbl 0598.47016

It is proved that a bounded operator on Hilbert space is the sum of two quasi-nilpotent operators if and only if it is not a non-zero scalar plus a compact operator. Necessary conditions and sufficient conditions for an operator to be the product of two quasi-nilpotent operators are given.

MSC:

47A65 Structure theory of linear operators
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