School of Mathematics
School of Mathematics
Course 415 - Topics in Analysis (Operator Theory)
2003-04 (JS & SS Mathematics
)
Lecturer: Dr. R. Hügli
Requirements/prerequisites: 321
Duration: 21 weeks
Number of lectures per week: 3 including tutorials
Assessment: No continuous assessment.
End-of-year Examination: 3-hour end of year examination.
Description:
The syllabus may be adjusted in the light of time constraints.
- Hilbert spaces: Orthonormal bases, projections,
self-adjoint and normal operators.
- Banach spaces: Bounded linear maps, linear functionals,
duality, the adjoint of an operator.
- Banach algebras: Ideals, spectrum, functional calculus,
speactral theory.
- C^{*}-algebras: Functional calculus, positive elements,
GNS-representation.
- von Neumann algebras: Topologies on B(H) (weak and
strong operator topologies), Abelian von Neumann algebras,
projections, traces.
Textbooks: The following will be used as a basis for most of the
topics.
John B. Conway, A Course in Functional Analysis. Second
Edition.
Graduate Texts in Mathematics Volume 96,
Springer-Verlag
(1990).
Oct 3, 2003
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