Ordered Banach Spaces and Positive Operators
4 April - 13 July 2023
Lecturer: Jochen Glück
On-site lectures at the University of Wuppertal:
- Tuesday, 12:15 - 14:00 in G.10.03 (lecture hall 08)
- Thursday, 12:15 - 14:00 in G.10.03 (lecture hall 08)
(all times in German local time = UTC+2)
Online live stream of the lectures:
(Please log-in to Zoom first in order to be able to access the session.)
Recordings of the lectures:
- Lecture 1 (2023-04-04, Section 1.1)
- Lecture 2 (2023-04-06, Section 1.2 - Proposition 1.4.6)
- Lecture 3 (2023-04-11, Proposition 1.4.3 to Proposition 1.5.3)
- Lecture 4 (2023-04-13, proof of Proposition 1.5.3 to Proposition 2.1.2)
- Lecture 5 (2023-04-18, Definition 2.1.3 to Example 2.1.8 (first part))
- Lecture 6 (2023-04-20, Example 2.1.8 (second part) to Theorem 2.2.5)
- Lecture 7 (2023-04-25, Examples 2.2.6 to Theorem 2.3.2)
- Lecture 8 (2023-04-27, Theorem 2.3.3 to Proposition 3.2.3 (statement only); Section 2.4 was skipped)
- Lecture 9 (2023-05-02, Proposition 3.2.3 to Corollary 3.2.6 (statement only))
- Lecture 10 (2023-05-04, Corollary 3.2.6 to Theorem 3.4.2)
- Lecture 11 (2023-05-09, Theorem 3.4.1 (proof) to Theorem 3.5.5)
- Lecture 12 (2023-05-12, beginning of Chapter 4 to Theorem 4.2.1)
- Lecture 13 (2023-05-16, beginning of Corollary 4.2.2 to Theorem 4.2.6)
- Lecture 14 (2023-05-25, Definition 4.3.1 to Corollary 4.4.1)
- Lecture 15 (2023-05-26, Proposition 4.4.2 to Proposition 5.1.5)
- Lecture 16 (2023-06-07, Definition 5.1.6 to Proposition 5.1.9)
- Lecture 17 (2023-06-13, Proof of Proposition 5.1.9 to Example 5.1.17)
- Lecture 18 (2023-06-15, Lemma 5.1.18 to Theorem 5.2.2)
- Lecture 19 (2023-06-20, Proof of Theorem 5.2.2)
- Lecture 20 (2023-06-22, Lemma 5.2.3 to Theorem 6.1.2)
- Lecture 21 (2023-06-27, Proof of Theorem 6.1.2 to Theorem 6.2.5)
- Lecture 22 (2023-06-29, Theorem 6.3.1 to Proposition 7.1.3)
- Lecture 23 (2023-07-04, Proposition 7.1.3 to Definition 7.1.6)
- Lecture 24 (2023-07-06, Theorem 7.2.1 to Theorem 7.2.5)
Weekly exercise classes will take place at the University of Wuppertal and at the Technical University of Dresden.
- On-site: Wednesday, 16:00 - 18:00 in G.15.34
- The exercise class in Wuppertal will neither be streamed nor recorded.
- First exercise class: Wednesday, 12 April 2023
- Responsible for the exercise class: Julian Hölz
- On-site: Tuesday, 09:20 - 10:50 in GER/051
- The exercise class in Dresden will be streamed but not be recorded.
- Please send an email to Florian Boisen (florian.boisen "at" mailbox.tu-dresden.de) to get access to the link of the stream and to get further information on the exercise class.
- First exercise class: 11 April 2023
- Responsible for the exercise class: Anke Kalauch and Florian Boisen
Access to the lecture notes requires a password (to prevent numerous different and uncomplete versions of the lecture notes from getting indexed by search engines). To get the password you can (i) attend the first lecture or (ii) watch the (publicly available) recording of first lecture or (iii) write an email to Jochen Glück (glueck "at" uni-wuppertal.de).
The lecture notes are updated and completed on the fly. The final version will be uploaded here at the end of the course and will be accessible without password.
Weekly problem sheets:
- Sheet 1__correction (Solutions)
- Sheet 2 (Solutions)
- Sheet 3 (Solutions)
- Sheet 4__correction2 (Solutions)
- Sheet 5 (Solutions)
- Sheet 6 (Solutions)
- Sheet 7 (Solutions)
- Sheet 8 (Solutions)
- Sheet 9 (Solutions)
- Sheet 10__correction (Solutions)
- Sheet 11 (Solutions)
- Sheet 12 (Solutions)
- Sheet 13 (Solutions)
Many Banach spaces that occur in applications and concrete examples carry a partial order. For instance, elements of function spaces can be compared componentwise, functions in L^p-spaces can be compared almost everywhere, and self-adjoint operators on Hilbert spaces can be partially ordered by their spectral properties.
The theory of ordered Banach spaces is a general framework to analyze such order structures. The course starts with a basic introduction to the theory and later toches on recent research topics.
Basic knowledge of functional analysis (for instance from an introductory course to functional analysis) is required.
Information for students from Wuppertal:
Knowledge from the course Funktionalanalysis 1 is not required. It suffices if you have attended Grundlagen der Funktionalanalysis.
Organizational information for students from Wuppertal
If you are a studend at University of Wuppertal and participate in the course, please register in the corresponding moodle course (such that we can reach you via email):
Eligible as one of the following modules:
The lecture is designed for Master's (and PhD) students. If you are a Master's student iat University of Wuppertal and take and pass an oral exam at the end of the semster, the lecture can be counted as one of the following modules:
- Funktionalanalysis 2
- Spezielle Kapitel der Funktionalanalysis
- Spezielle Kapitel der Reinen Mathematik