Initial results connect Krylov solvability in Banach spaces to spectral theory via resolvent operators.
Saad , Iterative methods for sparse linear systems , Society for Industrial and Applied Mathematics, Philadelphia, PA, second ed
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Some results on Krylov solvability in Banach space and connections to spectral theory
Initial results connect Krylov solvability in Banach spaces to spectral theory via resolvent operators.