Teoremi di convergenza in teoria della misura non commutativa
The bundle convergence in von Neumann algebras and their -spaces
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
The distribution of non-commutative Rademacher series.
The Lévy-Khintchine formula and Nica-Speicher property for deformations of the free convolution
We study deformations of the free convolution arising via invertible transformations of probability measures on the real line T:μ ↦ Tμ. We define new associative convolutions of measures by . We discuss infinite divisibility with respect to these convolutions, and we establish a Lévy-Khintchine formula. We conclude the paper by proving that for any such deformation of free probability all probability measures μ have the Nica-Speicher property, that is, one can find their convolution power for...
The monotone cumulants
In the present paper we define the notion of generalized cumulants which gives a universal framework for commutative, free, Boolean and especially, monotone probability theories. The uniqueness of generalized cumulants holds for each independence, and hence, generalized cumulants are equal to the usual cumulants in the commutative, free and Boolean cases. The way we define (generalized) cumulants needs neither partition lattices nor generating functions and then will give a new viewpoint to cumulants....
The monotone Poisson process
The coefficients of the moments of the monotone Poisson law are shown to be a type of Stirling number of the first kind; certain combinatorial identities relating to these numbers are proved and a new derivation of the Cauchy transform of this law is given. An investigation is begun into the classical Azéma-type martingale which corresponds to the compensated monotone Poisson process; it is shown to have the chaotic-representation property and its sample paths are described.
The noncommutative Hilbert transform approach to free entropy
The Powers sum of spatial CPD-semigroups and CP-semigroups
We define spatial CPD-semigroups and construct their Powers sum. We construct the Powers sum for general spatial CP-semigroups. In both cases, we show that the product system of that Powers sum is the product of the spatial product systems of its factors. We show that on the domain of intersection, pointwise bounded CPD-semigroups on the one side and Schur CP-semigroups on the other, the constructions coincide. This summarizes all known results about Powers sums and generalizes them considerably....
The Radon-Nikodym Theorem for Weights on Semi-Finite JBW-Algebras.
The simplex of tracial quantum symmetric states
We show that the space of tracial quantum symmetric states of an arbitrary unital C*-algebra is a Choquet simplex and is a face of the tracial state space of the universal unital C*-algebra free product of A with itself infinitely many times. We also show that the extreme points of this simplex are dense, making it the Poulsen simplex when A is separable and nontrivial. In the course of the proof we characterize the centers of certain tracial amalgamated free product C*-algebras.
The trace of finite and nuclear elements in Banach algebras
The unconditional pointwise convergence of orthogonal seriesin over a von Neumann algebra
The paper is devoted to some problems concerning a convergence of pointwise type in the -space over a von Neumann algebra M with a faithful normal state Φ [3]. Here is the completion of M under the norm .
The -deformation of the classical convolution
We study deformations of the classical convolution. For every invertible transformation T:μ ↦ Tμ, we are able to define a new associative convolution of measures by . We deal with the -deformation of the classical convolution. We prove the analogue of the classical Lévy-Khintchine formula. We also show the central limit measure, which turns out to be the standard Gaussian measure. Moreover, we calculate the Poisson measure in the -deformed classical convolution and give the orthogonal polynomials...
Traces on JW-Algebras and Enveloping W*-Algebras.
Transition probabilities and trace functions for C*-algebras.
Two-level t-deformation
In the present paper we define and study the properties of a deformation of measures and convolutions that works in a similar way to the deformation of Bożejko and Wysoczański, but in its definition operates on two levels of Jacobi coefficients of a measure, rather than on one.
Two-valued measures on -classes