1. Spaces
2. Normal Spaces
3. Sequence Space
4. Finite Dimensional Space
5. Finite Dimensional Normal Space
6. Norm of a Linear Operator
7. Dual Basis
8. The Space of Bounded Linear Operators (Functionals)
9. Inner Product Space
10. Minimizing Vector
11. Orthonormal Sequences and Sets
12. Fourier Series
13. Parseval Relationship
14. Riesz Representation Theorem
15. Sesquilinear Forms
16. Hamel Basis of a Vector Space
17. Sublinear Functions
18. Hahn-Banach Theorem
19. Complex Linearity
20. Application of Hahn-Banach Theorem
21. Bounded Variations
22. Reflexive Spaces
23. Category Theorem
24. Uniform Boundedness Theorem
25. Weak Convergence
26. Weak Convergence II
27. Closed Operators
28. Spectral Theory in Finite Dimension
29. Spectral Theory

Taught by Dr. Greg Morrow, Math 535, Applied Functional Analysis is an introduction to the basic concepts, methods and applications of functional analysis. Topics covered will include metric spaces, normed spaces, Hilbert spaces, linear operators, spectral theory, fixed point theorems and approximation theorems.

From the UCCS math department course catalog, the list of topics is: Basic concepts, methods, and applications of functional analysis. Complete metric spaces, contraction mapping, and applications. Banach spaces and linear operators. Inner product and Hilbert spaces, orthonormal bases and expansions, approximation, and applications. Spectral theory of compact operators, including self adjoint and normal operators.

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