5811 ريض (التحليل الدالي I) (مقرر سابق)

Vector spaces, Normed spaces, Banach spaces: basic properties and examples, convex sets, subspaces and quotient spaces, linear functionals and dual spaces. Fundamental theorems: 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, projections, self-adjoint operators, normal operators, isometric and unitary operators, positive operators and polar decomposition.
References

1) E. Kreyszig:  A Introductory functional analysis with applications. John Wiley & Sons 1978.

2)  G.F. Simmons: Introduction to topology and modern analysis. Krieger Publishing Company 1963.

3) J.B. Conway: A Course in Functional Analysis, Springer-Verlag, New-York, Second edition 1997