A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F23%3AA0000145" target="_blank" >RIV/47813059:19610/23:A0000145 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11785-023-01413-0" target="_blank" >https://link.springer.com/article/10.1007/s11785-023-01413-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11785-023-01413-0" target="_blank" >10.1007/s11785-023-01413-0</a>
Alternative languages
Result language
angličtina
Original language name
A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space
Original language description
We analyse the Krylov solvability of inverse linear problems on Hilbert space H where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound implications in theoretical and applied numerical analysis as it is critical to understand the utility of Krylov based methods for solving inverse problems. Our results explicitly describe for the first time the Krylov subspace for such operators given any datum vector g is an element of H, as well as prove that all inverse linear problems are Krylov solvable provided that g is in the range of such an operator. We therefore expand our knowledge of the class of Krylov solvable operators to include the normal compact operators. We close the study by proving an isomorphism between the closed Krylov subspace for a general bounded normal operator and an L-2-measure space based on the scalar spectral measure.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Complex Analysis and Operator Theory
ISSN
1661-8254
e-ISSN
1661-8262
Volume of the periodical
17
Issue of the periodical within the volume
7
Country of publishing house
CH - SWITZERLAND
Number of pages
12
Pages from-to
„109-1“-„109-12“
UT code for WoS article
001066912100001
EID of the result in the Scopus database
2-s2.0-85171555783