Elke Enning

Dmitri Pavlov (University of California, Berkeley): Tensor products of noncommutative Lp-spaces and equivalences of categories of Lp-modules. Oberseminar C*-Algebren.

Tuesday, 20.10.2009 15:15 im Raum N3 (Neubau)

Mathematik und Informatik

In the first part of this talk I will introduce Haagerup's theory of noncommutative Lp-spaces using the nice algebraic formalism of modular algebras by Yamagami. (Here Lp=L^{1/p}, in particular, L_0=L^\infty and L1/2=L2.) Then I will discuss some interesting properties of the resulting Lp-spaces, in particular I will prove the following theorem: Lp(M)\otimes_M Lq(M)=Lp+q(M) for an arbitrary von Neumann algebra~M and arbitrary complex p and q with nonnegative real parts. Equality here means isometric isomorphism of M-M-bimodules. In the second part of the talk I will describe Lp-modules by Junge and Sherman, which are the noncommutative analogs of modules of p-sections of bundles of Hilbert spaces over a measurable space. The special cases p=0 and p=1/2 correspond to the well-known cases of Hilbert W*-modules and Connes' correspondences. I will prove that W*-categories of Lp-modules for all values of~p are equivalent to each other. After that I will explain how Connes' fusion (and its generalized version), which originally had very technical definition, can be described easily in this algebraic formalism.

Angelegt am Friday, 16.10.2009 12:09 von Elke Enning
Geändert am Friday, 16.10.2009 12:09 von Elke Enning
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