Reading group: Operator spaces
Wintersemester 2015/16
Objective
The goal of this reading group is to familiarize ourselves with the theory of operator spaces. We will closely follow Paulsen's book initially. Some recent applications to quantum information science will be discussed subsequently.
Literature
- Ron C. Blei: An elementary proof of the Grothendieck inequality
, Proc. Amer. Math. Soc. 100 (1987), 58-60
- Edward Effros, Zhong-Jin Ruan: Operator spaces, Oxford Science Publications, 2000
- Vern Paulsen: Completely Bounded Maps and Operator Algebras, Cambridge Studies in Advanced Mathematics, 2003
- Carlos M. Ortiz, Vern I. Paulsen: Lovász theta type norms and Operator Systems
- Runyao Duan, Simone Severini, Andreas Winter: Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function
- Carlos Palazuelos, Thomas Vidick: Survey on Nonlocal Games and Operator Space Theory
- Gilles Pisier: Introduction to Operator Space Theory, Cambridge University Press, 2003
List of talks
- 10.9. Operator spaces (Milan Mosonyi)
- 13.10. Choi isomorphism
- 20.10. Choi-Effros Theorem
- 27.10. Arveson's extension theorem (Martin Idel)
- 3.11. Net convergence
- 10.11. Arveson's extension theorem continued
- 10.11. Completely bounded maps (Stefan Huber)
- 19.11. Completely bounded maps continued
- 26.11. Graph theory and operator systems with applications to capacities (Daniel Stilck França)
- 10.12. Tensor products of Banach spaces (Milan Mosonyi)
- 21.1. Tensor product of operator spaces (Andreas Bluhm)
- 28.1. Dual space of operator spaces
- 11.2. XOR games, non-local games and operator space theory (Anna-Lena Hashagen)
- 16.2. Operator space structure on \ell^n_\infinity, dual spaces, bilinear forms and tensor products (Milan Mosonyi)
- 23.2. Minimal tensor product of operator spaces, continued (Milan Mosonyi)
- 23.2. Discrete version of Groethendieck's inequality (Daniel Stilck França)
