About: An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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) Je dokázáno, že operátor na Hilbertově prostoru je součinem dvou quasinilpotentních operátorů právě když není semi-Fredholmův. To řeší problém Fonga a Sourora z roku 1984. (cs)
Title	An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm Operátor je součinem dvou quasinilpotentů právě když není semi-Fredholmův (cs) An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm (en)
skos:prefLabel	An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm Operátor je součinem dvou quasinilpotentů právě když není semi-Fredholmův (cs) An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm (en)
skos:notation	RIV/67985840:_____/06:00047586!RIV07-AV0-67985840
http://linked.open.../vavai/riv/strany	935;944
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/03/0041), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2007
http://linked.open...aciTvurceVysledku	Müller, Vladimír
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	464827
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/06:00047586
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	products of operators; nilpotent operators; quasinilpotent operators (en)
http://linked.open.../riv/klicoveSlovo	nilpotent operators products of operators quasinilpotent operators
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[2D23D49A5555]
http://linked.open...i/riv/nazevZdroje	Proceedings of the Royal Society of Edinburgh. A - Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Methods and function theory of Banach algebras in operator theory II.
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	136A
http://linked.open...iv/tvurceVysledku	Müller, Vladimír Drnovšek, R. Novák, N.
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	0308-2105
number of pages	10 (xsd:int)

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