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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F06%3A00047586%21RIV07-AV0-67985840
rdf:type
n5:Vysledek skos:Concept
dcterms:description
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. 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.
dcterms: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 An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm
skos:prefLabel
An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm 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
skos:notation
RIV/67985840:_____/06:00047586!RIV07-AV0-67985840
n3:strany
935;944
n3:aktivita
n10:P n10:Z
n3:aktivity
P(GA201/03/0041), Z(AV0Z10190503)
n3:cisloPeriodika
5
n3:dodaniDat
n16:2007
n3:domaciTvurceVysledku
n18:8840199
n3:druhVysledku
n4:J
n3:duvernostUdaju
n17:S
n3:entitaPredkladatele
n11:predkladatel
n3:idSjednocenehoVysledku
464827
n3:idVysledku
RIV/67985840:_____/06:00047586
n3:jazykVysledku
n15:eng
n3:klicovaSlova
products of operators; nilpotent operators; quasinilpotent operators
n3:klicoveSlovo
n12:products%20of%20operators n12:quasinilpotent%20operators n12:nilpotent%20operators
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[2D23D49A5555]
n3:nazevZdroje
Proceedings of the Royal Society of Edinburgh. A - Mathematics
n3:obor
n7:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:projekt
n8:GA201%2F03%2F0041
n3:rokUplatneniVysledku
n16:2006
n3:svazekPeriodika
136A
n3:tvurceVysledku
Novák, N. Drnovšek, R. Müller, Vladimír
n3:zamer
n14:AV0Z10190503
s:issn
0308-2105
s:numberOfPages
10