1. Vectors.- 2. Spaces.- 3. Weak Topology.- 4. Analytic Functions.- 5. Infinite Matrices.- 6. Boundedness and Invertibility.- 7. Multiplication Operators.- 8. Operator Matrices.- 9. Properties of Spectra.- 10. Examples of Spectra.- 11. Spectral Radius.- 12. Norm Topology.- 13. Operator Topologies.- 14. Strong Operator Topology.- 15. Partial Isometries.- 16. Polar Decomposition.- 17. Unilateral Shift.- 18. Cyclic Vectors.- 19. Properties of Compactness.- 20. Examples of Compactness.- 21. Subnormal Operators.- 22. Numerical Range.- 23. Unitary Dilations.- 24. Commutators.- 25. Toeplitz Operators.- References.- List of Symbols.
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