Initial results connect Krylov solvability in Banach spaces to spectral theory via resolvent operators.
Kato , Perturbation theory for linear operators , Classics in Mathematics , Springer-Verlag, Berlin
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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.