J
2023
A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space
CARUSO, Noe Angelo
Basic information
Original name
A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space
Authors
CARUSO, Noe Angelo (36 Australia, guarantor, belonging to the institution)
Edition
Complex Analysis and Operator Theory, Basel, Switzerland, Springer Basel AG, 2023, 1661-8254
Other information
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
Switzerland
Confidentiality degree
není předmětem státního či obchodního tajemství
RIV identification code
RIV/47813059:19610/23:A0000145
Organization unit
Mathematical Institute in Opava
Keywords in English
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
Tags
International impact, Reviewed
V originále
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.
Displayed: 24/12/2024 04:25