1. Metric Spaces2. Normed Spaces. Banach Spaces3. Inner Product Spaces. Hilbert Spaces4. Fundamental Theorems for Normed and Banach Spaces5. Further Applications: Banach Fixed Point Theorem6. Further Applications: Approximation Theory7. Spectral Theory of Linear Operators in Normed Spaces8. Compact Linear Operators on Normed Spaces and Their Spectrum9. Spectral Theory of Bounded Self-Adjoint Linear Operators10. Unbounded Linear Operators in Hilbert Space11. Unbounded Linear Operators in Quantum ...
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