Oberseminar C*-Algebren. Uffe Haagerup: Dilation problems for completely positive maps on von Neumann algebras.
Tuesday, 28.04.2009 15:15 im Raum SFB
Abstract:
The talk is based on a joint work in progress with Magdalena Musat. We
study two dilation properties for completely positive unital trace preserving
maps (for short, cp.u.t. maps) on (M, tr), where M is a von Neumann
algebra and tr is a normal faithful trace state on M.
The first property is Kümmerer's Markov dilation property from the 80's,
which is equivalent to Anantharaman-Delaroche's factorization property from
2004. For this, we provide, for instance, an example of one-parameter
semigroup (T_t)_t >= 0 of cp.u.t. maps on the 4 x 4 matrices such that T_t
fails to have the Markov dilation property for all small values of t > 0.
The second property is the non-commutative Rota dilation property
introduced by Junge, Le Merdy and Xu in 2006. We show that the most
natural generalization of Rota's classical dilation theorem to the
non-commutative setting does not hold by providing an example of a
selfadjoint cp.u.t. map T on the n x n matrices for some large n, such that
T2 does not have the non-commutative Rota dilation property.
Angelegt am 22.04.2009 von Elke Enning
Geändert am 22.04.2009 von Elke Enning
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