國立清華大學數學系
泛函分析二
Math 5040-00 (Spring 2015) Functional Analysis II
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Office: 綜三 609 |
Course
Description:
This is a continuation of
the course Functional Analysis I (Math 5030-00), in which we have covered
several fundamental concepts and theorems of Hilbert spaces, Banach spaces, and bounded linear operators. Topics to be included in the second semester
are:
1. Examples of bounded
linear operators
2. Banach
algebra, Gelfand’s theory
3. Examples of operators and
their spectra
4. Compact operators
5. Fredholm’s
theory
6. Invariant subspaces
7. Compact symmetric
operators (if time permits)
This course is intended for
graduate students and advanced undergraduate students who have moderate
acquaintance on Hilbert and Banach space theories,
such as Hahn-Banach theorem, open mapping and closed
graph theorems, uniform boundedness principle, weak
and weak* topologies, convexity and Krein-Milman
theorem. Those who wish to take this course but have never taken Functional
Analysis I are advised to consult with me before or during the first week of
classes. Due to conflict with a national holiday and a school event, there will be no classes on 2/27 and 3/6.
To make up the classes, we will first
meet on 3/2, 14:20-17:20.
Textbook:
P.D.Lax: Functional Analysis, Wiley, 2002.
Primary
References:
1. J.B.Conway:
A Course in Functional Analysis, Second edition, Springer-Verlag,
1990.
2. E.M.Stein
& R.Shakarchi: Functional Analysis: Introduction
to Further Topics in Analysis, Princeton University Press, 2011.
Grading:
Homework assignments: 70%
Final exam: 30%
Attendance:
Students are expected to attend every scheduled
class. It is the student's responsibility to keep informed of any
announcements, syllabus adjustments or policy changes made during scheduled
classes.