Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pe lczynski subsequence decomposition of bounded sequences in L[0, 1] to the case of the Haagerup L-spaces (1 ≤ p < ∞). In particular, we prove that if (φn)n is a bounded sequence in the predual M∗ of M, then there exist a subsequence (φnk)k of (φn)n, a decomposition φnk = yk + zk su...

X iv :m at h/ 04 09 13 9v 1 [ m at h. FA ] 8 S ep 2 00 4 A WEAK TYPE INEQUALITY FOR NON-COMMUTATIVE MARTINGALES AND APPLICATIONS NARCISSE RANDRIANANTOANINA Abstract. We prove a weak-type (1,1) inequality for square functions of noncommutative martingales that are simultaneously bounded in L and L. More precisely, the following non-commutative analogue of a classical result of Burkholder holds: ...

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of s...

The Stone spectrum of a von Neumann algebra is a generalization of the Gelfand spectrum, as was shown by de Groote. In this article we clarify the structure of the Stone spectra of von Neumann algebras of type In.

In this paper we show that the fundamental group !T of the von Neumann algebra 2(Foo) of a free (noncommutative) group with infinitely many generators is lR+ \ {O}. This extends the result of Voiculescu who previously proved [26,27] that Q+ \ {O} is contained in !T(2(Foo)). This solves a classical problem in the harmonic analysis of the free group F 00. In particular, it follows that there exis...

In this paper we show that the fundamental group !T of the von Neumann algebra 2(Foo) of a free (noncommutative) group with infinitely many generators is lR+ \ {O}. This extends the result of Voiculescu who previously proved [26,27] that Q+ \ {O} is contained in !T(2(Foo)). This solves a classical problem in the harmonic analysis of the free group F 00. In particular, it follows that there exis...

I. Jordan algebras in antiquity (1933-1966). I am unable to prove Jordan algebras were known to Archimedes, or that a complete theory has been found in the unpublished papers of Gauss. Their first appearance in recorded history seems to be in the early 1930's when the theory bursts forth full-grown from the mind, not of Zeus, but of Pascual Jordan, John von Neumann, and Eugene Wigner in their 1...