# Haagerup L^p spaces

Időpont:
2018. 09. 19. 16:00
Hely:
H306
Előadó:
Vrana Péter, BME Matematika Intézet

The goal of this talk is to give an introduction to Haagerup's
construction of an $L^p$ space associated with a von Neumann algebra.
Some background: Separable commutative von Neumann algebras are
isomorphic to $L^\infty(X,\mu)$ for some standard measure space, and to
such a space one associates the $L^p$ spaces in the usual sense. For a
semifinite von Neumann algebra $M$ with faithful normal semifinite trace
$\tau$, Dixmier, Segal and Kunze introduced a space $L^p(M,\tau)$,
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 $L^p(M,\tau)$ for any
faithful normal semifinite trace $\tau$.