Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Summary of prerequisite topics for MSc students: in addition to the Autumn-term Hilbert Space module: basics of Linear Algebra including unitary diagonalization; ideas from metric or normed spaces including continuity, completeness and compactness, orthogonal decompositions and orthogonal bases of Hilbert spaces.
Occurrence | Teaching cycle |
---|---|
A | Spring Term 2022-23 |
To explore the exotic world of linear operators in infinitely many dimensions.
To compare linear operators in finitely many and infinitely many dimensions.
To encounter specific applications of the general theory.
The definition and significance of bounded and compact operators.
The idea of the spectrum, and the difference between 'spectral point' and 'eigenvalue'.
The Spectral Theorem and functional calculus as a generalisation of the orthogonal diagonalisation theorem.
.
Syllabus
The algebra of bounded operators in a Hilbert space and the ideals of finite-rank, Hilbert-Schmidt and compact operators.
Definitions and properties of self-adjoint operators.
Spectral Theorem and functional calculus illustrated by compact normal operators or bounded self-adjoint operators.
Applications including differential or integral equations.
Task | Length | % of module mark |
---|---|---|
Closed/in-person Exam (Centrally scheduled) Functional Analysis |
2 hours | 100 |
None
Task | Length | % of module mark |
---|---|---|
Closed/in-person Exam (Centrally scheduled) Functional Analysis |
2 hours | 100 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
N Young, An Introduction to Hilbert Space, Cambridge University Press (S 7.82 YOU).
E Kreysig, Introductory Functional Analysis with Applications, Wiley (S 7.8 KRE).