Initial results connect Krylov solvability in Banach spaces to spectral theory via resolvent operators.
Whitley , Projecting m onto c_0 , The American Mathematical Monthly, 73 (1966), pp
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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.