Up: Teaching (past) 
Lecture Course: Functional Analysis
Mon, Wed 14  16 in B 005
 (20/02/09) Exams / Certificates
28 out of 42 participants of the exam on 07/02/09 have passed
the course.
You can pick up your exam and, if applicable, your certificate
in the office of Mrs Höchst (Room 330), beginning
Wed, 25 Feb 09. Please note that Bachelor students are not allowed
to take their exam home.
 (29/01/09) "Funktionalanalysis
II" (4+2 hours/week) in Summer 09
This course will be
continued next semester. Among others, we will cover the
following topics
 spectral theory of bounded selfadjoint operators
 unbounded operators, in particular symmetric
operators, quadratic forms,...
 spectral theory of unbounded operators
 Fourier transformation
 (19/01/09) Note on Exercise 40 on
Problem Sheet 12
The operators S and T are both linear. Invertibility of S
means that S, as given, is bijective.
 (14/01/09) Correction of
Theorem 4.23
Due to the problem with Theorem 4.23 which came up in class
today, I modified Definition 4.21 and Theorem 4.23 (which is
now 4.22). Examples 4.22 now come after the theorem as Remark
4.23. Please see the updated version with the definition of
reflexivity as part of Theorem 4.22.
 (09/01/09) Correction of Remark 2.37
The previous statement in part (b) on the inclusion of dual spaces
requires a dense(!) subspace Y. The conclusion in part (c)
was wrong! Please see the updated Remark 2.37 at the end of Sec. 2.4.
 (13/11/08) Correction of Lemma 1.64
Statement (iv) of Lemma 1.64, which was stated without proof
in class, is not true under the hypotheses of the Lemma. (Thanks
for pointing it out!) In fact, statement (iv) is a mere
reformulation of statement (iv)
of Lemma 65. Therefore it is equivalent to the validity of
Baire's theorem. Please see the corrected version of Section 1.7
below. In case this has affected your solution of Problem 16
(which is the proof of Lemma 1.65), you will still get full
credit, of course. The proof of Lemma 1.65 is now also available
in the script (p. 40).
 (24/10/08) Handing in of solutions to problem
sheets
Please note that you MUST hand in your solutions in teams of
two (neither one, nor three or more). We have absolutely no
capacity to correct more homework. Single returns will not
be corrected from problem sheet 2 on.
 (22/10/08) Comment on Exercise 8
– Problem Sheet 2:
Since we have not "officially" introduced
normed spaces so far, here is a reformulation of the
problem. Prove that the space
c_{o}, when equipped with the metric
d_{∞}, as defined in class, is a separable
metric space.
Literature
The course will not follow a particular textbook. The
following list provides a short selection of English and German
textbooks on the subject (of which there are many!). Most of them cover
the material of a twosemester course. One copy of each of the books
listed below is kept on reserve in the library on a separate shelf for
our course.

M Reed and B Simon, Methods of
modern Mathematical Physics I: Functional analysis, Academic
Press, 1980
excellent
textbook with a focus on spectral theory, beginning not very gentle,
proofs sometimes a bit brief, unfortunately
rather pricey

D
Werner, Einführung in die
Funktionalanalysis, Springer,
a German classic, covers
a broad range of topics, including historical remarks

M
Dobrowolski, Angewandte Funktionalanalysis, Springer, 2006
the basics of functional analysis plus a thorough
discussion of Sobolev spaces and elliptic PDE's

E Kreyszig, Introductory
functional analysis with applications, Wiley, 1978
thorough and
pedagogical, very explicit proofs, does not cover all topics treated in
the course (e.g. no L^{p}spaces)

P D Lax,
Functional Analysis, Wiley, 2002
well readable with an emphasis on spectral theory and
some applications to quantum mechanics

F
Hirzebruch and W Scharlau, Einführung in die Funktionalanalysis,
BI Mannheim, 1971
another German classic, elegant but very(!) concise
