An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F06%3A00047586" target="_blank" >RIV/67985840:_____/06:00047586 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
An operator is a product of two quasi-nilpotent operators if and only if it is not semi-Fredholm
Original language 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.
Czech name
Operátor je součinem dvou quasinilpotentů právě když není semi-Fredholmův
Czech 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.
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F03%2F0041" target="_blank" >GA201/03/0041: Methods and function theory of Banach algebras in operator theory II.</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2006
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the Royal Society of Edinburgh. A - Mathematics
ISSN
0308-2105
e-ISSN
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Volume of the periodical
136A
Issue of the periodical within the volume
5
Country of publishing house
GB - UNITED KINGDOM
Number of pages
10
Pages from-to
935-944
UT code for WoS article
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EID of the result in the Scopus database
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