A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space

@article{78286,
   author = {Caruso, Noe Angelo},
   article_location = {Basel, Switzerland},
   article_number = {7},
   doi = {http://dx.doi.org/10.1007/s11785-023-01413-0},
   keywords = {Bounded linear operators; Compact operators; Cyclic operators; Ill-posed problems; Infinite-dimensional Hilbert space; Inverse linear problems; Krylov solution; Krylov solvability; Krylov subspaces; Normal operators},
   language = {eng},
   issn = {1661-8254},
   journal = {Complex Analysis and Operator Theory},
   title = {A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space},
   url = {https://link.springer.com/article/10.1007/s11785-023-01413-0},
   volume = {17},
   year = {2023}
}

TY  - JOUR
ID  - 78286
AU  - Caruso, Noe Angelo
PY  - 2023
TI  - A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space
JF  - Complex Analysis and Operator Theory
VL  - 17
IS  - 7
SP  - "109-1"-"109-12"
EP  - "109-1"-"109-12"
PB  - Springer Basel AG
SN  - 16618254
KW  - Bounded linear operators
KW  - Compact operators
KW  - Cyclic operators
KW  - Ill-posed problems
KW  - Infinite-dimensional Hilbert space
KW  - Inverse linear problems
KW  - Krylov solution
KW  - Krylov solvability
KW  - Krylov subspaces
KW  - Normal operators
UR  - https://link.springer.com/article/10.1007/s11785-023-01413-0
N2  - 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.
ER  - 

CARUSO, Noe Angelo. A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space. \textit{Complex Analysis and Operator Theory}. Basel, Switzerland: Springer Basel AG, 2023, vol.~17, No~7, p.~''109-1''-''109-12'', 12 pp. ISSN~1661-8254. Available from: https://dx.doi.org/10.1007/s11785-023-01413-0.