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A comment on free group factors

Narutaka Ozawa (2010)

Banach Center Publications

Let M be a finite von Neumann algebra acting on the standard Hilbert space L²(M). We look at the space of those bounded operators on L²(M) that are compact as operators from M into L²(M). The case where M is the free group factor is particularly interesting.

A Note on L-sets

Gero Fendler (2002)

Colloquium Mathematicae

Answering a question of Pisier, posed in [10], we construct an L-set which is not a finite union of translates of free sets.

Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

Nico Spronk (2010)

Banach Center Publications

Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, L - 1 ( G ) and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for L - 1 ( G ) and M(G). For us, “amenability properties” refers to amenability, weak amenability, and biflatness, as well as some properties which...

Analytic semigroups on vector valued noncommutative L p -spaces

Cédric Arhancet (2013)

Studia Mathematica

We give sufficient conditions on an operator space E and on a semigroup of operators on a von Neumann algebra M to obtain a bounded analytic or R-analytic semigroup ( ( T I d E ) t 0 on the vector valued noncommutative L p -space L p ( M , E ) . Moreover, we give applications to the H ( Σ θ ) functional calculus of the generators of these semigroups, generalizing some earlier work of M. Junge, C. Le Merdy and Q. Xu.

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