Instructor: Marius Junge
 

Program:

I General theory

1) Introduction
2) Basic definitions
3) Bounded linear maps and dual spaces
4) Approximation numbers and Schatten classes*

* postponed

II Finite Dimensional Theory

1) The Lewis Lemma
2) The Banach Mazur compactum
3) Some norms for linear operators
4) Examples of trace duality
5) John's Elliposoid
6) Applications and Tomcak-Jaegermann's theorem
7) Unconditional convergence
8) Revisiting the approximation property
....

to be completed
 

1.  Homework due Wednesday 8/30

2.  Homework due Wednesday 9/6

3.  Homework due Wednesday 9/13

4.  Homework due Wednesday 9/13

5.  Homework due Wednesday 9/13

6.  Homework due Wednesday 9/13

7.  Homework due Wednesday 9/13

8.  Homework due Wednesday 9/13
 

Some solutions  and remarks:

1.  Solutions
 

Solutions involving completeness, Solutions involving completeness(pdf)
 

Np-Solutions by Anthony I and II

Office hours: by appointment

Text books:

G. Pisier: The Volume of Convex Bodies and Banach Space Geometry; Cambridge Tracts in     Mathematics 94, 1989.

J. Lindenstrauss and L. Tzafrir: Classical Banach Spaces I, II; Springer Verlag 1977, 1979.

V. Milman and G. Schechtmann: Asymptotic theory of finite dimensional normed spaces; Springer Lecture
 
 

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