Haagerup L^P Spaces

Időpont: 
2018. September 19. 16:00
Helyszín: 
H building, room 306
Kategória: 
Előadás
Szervezés: 
BME-egyetem
Kapcsolattartó: 
Department of Analysis
Lecturer: : Vrana Péter, Institute of Mathematics
 
The goal of this talk is to give an introduction to Haagerup's construction of an Lp space associated with a von Neumann algebra. Some background: Separable commutative von Neu0mann algebras are isomorphic to L∞(X,μ) for some standard measure space, and to such a space one associates the Lp spaces in the usual sense. For a semifinite von Neumann algebra M with faithful normal semifinite trace τ, Dixmier, Segal and Kunze introduced a space Lp(M,τ), generalizing the classical ones. The extension by Haagerup applies to arbitrary (not necessary semifinite) von Neumann algebras and for semifinite ones it is isometrically isomorphic to Lp(M,τ) for any faithful normal semifinite trace τ.