A note on the Krylov solvability of compact normal operators on Hilbert space

Noe Angelo Caruso

Published 2022-10-10Version 1

We analyse the Krylov solvability of inverse linear problems on Hilbert space $\mathcal{H}$ where the underlying operator is compact and normal. Our results explicitly describe the Krylov subspace for such operators given any datum vector $g\in\mathcal{H}$, as well as prove that all inverse linear problems are Krylov solvable provided that $g$ is in the range of the operator. 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.