Preface
1. Basic inequalities
2. Normed spaces and bounded linear operators
3. Linear functional and the Hahn-Banach theorem
4. Finite-dimensional normed spaces
5. The Baire category theorem and the closed-graph theorem
6. Continuous functions on compact spaces and the Stone-Weierstrass theorem
7. The contraction-mapping theorem
8. Weak topologies and duality
9. Euclidean spaces and Hilbert spaces
10. Orthonormal systems
11. Adjoint operators
12. The algebra of bounded linear operators
13. Compact operators on Banach spaces
14. Compact normal operators
15. Fixed-point theorems
16. Invariant subspaces
Index of notation
Index of terms.
