| Instructor | | Volker Runde |
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| Office hours | | By appointment and via Google Meet only. |
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| Course Content | |
This course is a second course in functional analysis and explores topics that were only touched upon in MATH 516 in greater depth. Topics to be covered are:
- locally convex spaces;
- weak and weak* topologies for Banach spaces;
- weak compactness in Banach spaces;
- classical Banach spaces and their structure;
- local structure of Banach spaces;
- infinite-dimensional geometry;
- tensor products of Banach spaces.
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| Prerequisites | | MATH 516 and MATH 447 (or equivalent). All the required background can be found in:
- V. Runde, A Taste of Topology (corrected 2nd printing). Springer Verlag, 2008.
- D. R. Farenick, Fundamentals of Functional Analysis. Springer Verlag, 2016.
As the course progresses, I will put my own course notes into LaTeX and make them available online.
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| Textbooks | | None required, but the following are recommended:
- J. B. Conway, A Course in Functional Analysis. Springer Verlag, 1985.
- M. Fabian et al., Functional Analysis and Infinite-Dimensional Geometry. Canadian Mathematical Society, 2001.
- W. Rudin, Functional Analysis. McGraw-Hill, 1991.
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| Grading | | The grade will be based on four homework assignments (altogether 50%) and a take home final (50%). The solutions have to be submitted through Assign2. |