On measure for projectors
An example of a finite set of projectors in is exhibited for which no 0-1 measure exists.
On measure for projectors. II
On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions
In this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko–Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.
On asymptotic growth of the support of free multiplicative convolutions.
On basic concepts of non-commutative topology
On homomorphisms of projective lattices in complex Hilbert spaces
On limits of -norms of linear operators
On some generalization of the t-transformation
Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation of probability measures on the real line ℝ, which is another possible generalization of the t-transformation. Using that deformation we define a new convolution by deformation of the free convolution. The central limit measure with respect to the -deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the two parameters...
On the Choquet and Bishop-de Leeuw theorems
On the convergence of operators
On the function .
On the law of large numbers for free identically distributed random variables.
On the Lebesgue decomposition of Gleason measures
On the Lebesgue decomposition of the normal states of a JBW-algebra
In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.
On the Lukacs property for free random variables
The Lukacs property of the free Poisson distribution is studied. We prove that if free and are free Poisson distributed with suitable parameters, then + and are free. As an auxiliary result we compute the joint cumulants of and for free Poisson distributed . We also study the Lukacs property of the free Gamma distribution.
Operators from C*-algebras to Banach Spaces.
Operator-valued version of conditionally free product
We present an operator-valued version of the conditionally free product of states and measures, which in the scalar case was studied by Bożejko, Leinert and Speicher. The related combinatorics and limit theorems are provided.
Order Derivations on Lp-Spaces of W*-Algebras.
Order properties of compact maps on L...-spaces associated with von Neumann algebras.
Orthogonal scalar products on von Neumann algebras