Banach fixed point theorem -- ch. 6. Further applications: approximation theory -- ch. 7. Spectral theory of linear operators in Normed spaces -- ch. 8. Compact linear operators on Normed spaces and their spectrum -- ch. 9. Spectral theory of bounded self-adjoint linear operators -- ch. 10. Unbounded linear operators in Hilbert space -- Unbounded linear operators in quantum mechanics.
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