(16 Dec 04)

MA4211 Functional Analysis

Modular credits: 4

Workload: 3-1-0-0-6

Pre-requisite(s): MA3207H or MA3209

Preclusion(s): FASS students of cohorts 1998, 1999 and 2000, FASS students from 2003 cohort onwards who major in Mathematics (for breadth requirement).

This course is for students who are majors in pure mathematics or who need functional analysis in their applied mathematics courses. The objective of the module is to study linear mappings defined on Banach spaces and Hilbert spaces, especially linear functionals (real-valued mappings) on L(p), C[0,1] and some sequence spaces. In particular, the four big theorems in functional analysis, namely, Hahn-Banach theorem, uniform boundedness theorem, open mapping theorem and Banach-Steinhaus theorem will be covered.

Major topics: Normed linear spaces and Banach spaces. Bounded linear operators and continuous linear functionals. Dual spaces. Reflexivity. Hanh-Banach Theorem. Open Mapping Theorem. Uniform Boundedness Principle. Banach-Steinhaus Theorem. The classical Banach spaces : c₀, l_p, L_p, C(K). Compact operators. Inner product spaces and Hilbert spaces. Orthonormal bases. Orthogonal complements and direct sums. Riesz Representation Theorem. Adjoint operators.