Math 5811

MATH5811 Functional Analysis 4(3+1)

Banach spaces: Basic properties and examples, convex sets, subspaces and quotient spaces, linear functional and the dual spaces, Hahn-Banach theorem, the uniform boundedness principle, the open mapping theorem and closed graph theorem, Hilbert spaces: the Riesz representation theorem, orthonormal bases, isomorphic Hilbert spaces, Operators on Hilbert spaces: Basic properties and examples, adjoints, projection, invariant and reducing subspaces, positive operators and the polar decomposition, self-adjoint operators, normal operators, isometric and unitary operators, the spectrum and the numerical range of an operator.
 

 

• 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.