Atlas: On the local structure of non-commutative $L

Atlas home || Conferences | Abstracts | about Atlas

Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

View Abstracts
Conference Homepage

On the local structure of non-commutative L₁-spaces
by
Edward Effros
University of California, Los Angeles

Operator algebra theory provides a mathematical context in which to study the non-commutative random variables of quantum physics. From the beginning it was understood that all of the "classical" Banach spaces have operator analogues, and that in particular, the preduals of von Neumann algebras play the role of the non-commutative L₁ spaces. On the other hand, it has become apparent that linear spaces of bounded Hilbert space operators provide the natural analogues of arbitrary Banach spaces.

As in Banach space theory, the non-commutative L₁ spaces are essential in the classification of operator spaces. Only recently it has been discovered that their local structure is surprisingly well-behaved. We will discuss various aspects of this phenomenon, including strong local reflexivity (Effros-Junge-Ruan) and Ozawa's recent results. We will also explore the possibility that these spaces might be used as an approach to a general classification theory for von Neumann algebras.

(T)

Date received: April 17, 2000