MATP15 Linear Functional Analysis
is an optional course for a Master of Science degree in mathematics.
Functional Analysis is the language of modern Analysis and as such it
appears in almost any related context. The course covers the basics of
the discipline: The Hahn-Banach Theorem, normed spaces, Hilbert spaces,
Banach spaces and their duals, reflexive spaces, weak and weak-star
convergence (topologies), the Banach-Alaoglu Theorem, basic theory of
bounded linear maps, compact maps and their spectral theory, and finally
the spectral theorem for compact symmetric maps on a Hilbert space.
The teaching consists of lectures, seminars.
The course is assessed through a written and an oral examination.
Peter D. Lax, Functional Analysis, (Wiley Pure and Applied Mathematics: A Series of Texts, Monographs and Tracts), 2002, ISBN: 978-0-471-55604-6.
The schedule is available in the TimeEdit
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