**Final Exam Schedule
**

**Spring 2007
****TMA4230: Functional Analysis **

The final exam, on May 18, will be oral and counts 80%. It will be held in the room 656 in “Sentralbygg 2”.

The oral examination will be as follows: First the student presents a mini lecture (20 minutes) on an assigned

topic, assigned from the list of topics below. Then questions from any parts of the syllabus are asked. Total

time: 40–45 minutes per student. Because there are many students and the schedule is tight, it is important

that you stay within your 20 minutes. You can bring and consult notes for your mini lecture. But all notes

have to be put away for the questions. Try to present the main result(s) with some proofs or bits of proof.

Obviously, you cannot present everything, but include what you think is most interesting or important.

The times and assigned topics for the oral examination will be as follows.

**
9:00: Stenseth, Hahan-Banach theorem for real vector spaces.
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9:45: Bø, The first geometric form of Hahn-Banach theorem.
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10:30: Bårtvedt, Krein-Milman theorem.
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11:15: Grøva, The principle of Uniform boundedness (Banach-Steinhaus theorem).
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13:00: Barker, Open mapping theorem.
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13:45: Eikrem, Closed graph theorem.
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14:30: Wiik, Non-emptiness of spectrum in Banach algebras (Gelfand's theorem).
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15:15: Skartsæterhagen, Spectral theorem for bounded selfadjoint operators.
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Please make sure to appear at the appointed time! And let me know as soon as possible if you are unable to come.
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Here are the final results after combination with the midterm grades:**

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Stenseth: C.
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Bø: C.
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Bårtvedt: did not attend.
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Grøva: did not attend.
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Barker:A.
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Eikrem: A.
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Wiik:A.
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Skartsæterhagen:C.
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