"Proceedings of the Royal Society of Edinburgh. A - Mathematics" . . . "An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm" . . "3"^^ . . "Nov\u00E1k, N." . "An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm"@en . "Je dok\u00E1z\u00E1no, \u017Ee oper\u00E1tor na Hilbertov\u011B prostoru je sou\u010Dinem dvou quasinilpotentn\u00EDch oper\u00E1tor\u016F pr\u00E1v\u011B kdy\u017E nen\u00ED semi-Fredholm\u016Fv. To \u0159e\u0161\u00ED probl\u00E9m Fonga a Sourora z roku 1984."@cs . "RIV/67985840:_____/06:00047586" . . "464827" . "Drnov\u0161ek, R." . . "Oper\u00E1tor je sou\u010Dinem dvou quasinilpotent\u016F pr\u00E1v\u011B kdy\u017E nen\u00ED semi-Fredholm\u016Fv"@cs . . "P(GA201/03/0041), Z(AV0Z10190503)" . "1"^^ . . "M\u00FCller, Vladim\u00EDr" . "136A" . "0308-2105" . . "RIV/67985840:_____/06:00047586!RIV07-AV0-67985840" . . . "An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm" . . "935;944" . "Oper\u00E1tor je sou\u010Dinem dvou quasinilpotent\u016F pr\u00E1v\u011B kdy\u017E nen\u00ED semi-Fredholm\u016Fv"@cs . "products of operators; nilpotent operators; quasinilpotent operators"@en . "An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm"@en . "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." . . . "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."@en . . . "10"^^ . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "[2D23D49A5555]" . . "5" .