An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm
2006 ◽
Vol 136
(5)
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pp. 935-944
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Keyword(s):
We prove that a (bounded, linear) operator acting on an infinite-dimensional, separable, complex Hilbert space can be written as a product of two quasi-nilpotent operators if and only if it is not a semi-Fredholm operator. This solves the problem posed by Fong and Sourour in 1984. We also consider some closely related questions. In particular, we show that an operator can be expressed as a product of two nilpotent operators if and only if its kernel and co-kernel are both infinite dimensional. This answers the question implicitly posed by Wu in 1989.
1969 ◽
Vol 21
◽
pp. 1421-1426
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1969 ◽
Vol 12
(5)
◽
pp. 639-643
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1989 ◽
Vol 32
(3)
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pp. 320-326
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Keyword(s):
2016 ◽
Vol 59
(2)
◽
pp. 354-362
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1974 ◽
Vol 76
(2)
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pp. 415-416
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