• MATH 581 Functional Analysis I 3 credit hours

Normed spaces, Banach spaces, continuous linear operators, Hahn-Banach theorem, Duality, the open mapping theorem, The closed graph theorem, the uniform boundedness theorem, Hilbert spaces, Adjoint operators, unitary and normal operators, projections, spectral theory in finite dimensional spaces, spectral properties of bounded linear operators.

• Main Reference

E. Kreyszig, "Introductory Functional analysis with Applications", John Wiley & sons, 1978

• Other References

1. J. Maddox, "Elements of Functional Analysis", Cambridge University Press, 1988.
2. W. Rudin, "Functional Analysis", McGraw-Hill, Inc., 1991.
3. G. F. Simmons, "Topology and Modern Analysis", McGraw-Hill, Inc., 1963.
4. C. Swarz, "An Introduction to Functional Analysis", Marcel Dekker, 1992.
5. Taylor and D. C. Lay, "Introduction to Functional Analysis", John Wiley & sons, 1980.
6. Y. C. Wong, "Introductory Theory of Topological Vector Spaces", Marcel Dekker, 1992.