Hilbert & Banach Spaces (U01878)

? Credit Points : 20 ? SCQF Level : 11 ? Acronym : MAT-4-HBS

Normed spaces and inner product spaces. Geometric and metric properties of Banach and Hilbert spaces. Orthogonal expansions and projections in Hilbert spaces. Bounded linear functionals and operators. Baire Category Theorem, Uniform Boundedness Principle and the Open Mapping Theorem. The spectral theorem for selfadjoint compact operators and applications to differential equations.

Entry Requirements

? Pre-requisites : MAT-3-CVD, MAT-3-PAA

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Full Year (Blocks 1-4)

? Contact Teaching Time : 2 hour(s) per week for 22 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	10:00	10:50	KB
Lecture	Thursday	10:00	10:50	KB

? Additional Class Information : In S2 moves to M&Th at 1210 hrs

Summary of Intended Learning Outcomes

1. Ability to apply general theory to specific examples.
2. Familiarity with abstract arguments.
3. An ability to use orthogonality arguments in concrete situations.
4. Familiarity of basic functional analysis results and an ability to use them.
5. To gain an appreciation of the interplay between analysis, geometry and algebra in the setting of Banach and Hilbert spaces.