Teoremi di convergenza in teoria della misura non commutativa
The arithmetic of distributions in free probability theory
We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and Schur functions. We consider the set of probability distributions as a semigroup M equipped with the operation of free convolution and prove a Khintchine type theorem for the factorization of elements of this semigroup. An element of M contains either indecomposable (“prime”) factors or it belongs to a class, say I 0, of distributions without indecomposable...
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 microstates free entropy dimension of any DT--operator is 2.
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 noncommutative Hilbert transform approach to free entropy
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...
The von Neumann algebras generated by -gaussians
We study the -deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if is sufficiently close to , then these algebras do not depend on . In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.
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-parameter non-commutative Central Limit Theorem
In 1992, Speicher showed the fundamental fact that the probability measures playing the role of the classical Gaussian in the various non-commutative probability theories (viz. fermionic probability, Voiculescu’s free probability, and -deformed probability of Bożejko and Speicher) all arise as the limits in a generalized Central Limit Theorem. The latter concerns sequences of non-commutative random variables (elements of a -algebra equipped with a state) drawn from an ensemble of pair-wise commuting...
Two-valued measures on -classes