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 automorphisms of type Arveson systems (probabilistic approach).
On basic concepts of non-commutative topology
On homomorphisms of projective lattices in complex Hilbert spaces
On limits of -norms of linear operators
On Markovian cocycle perturbations in classical and quantum probability.
On Neveu decomposition and ergodic type theorems for semi-finite von Neumann algebras.
On Ozeki's inequality.
On quantum extensions of the Azéma martingale semi-group
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 bundle convergence of double orthogonal series in noncommutative -spaces
The notion of bundle convergence in von Neumann algebras and their -spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men’shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series....
On the Choquet and Bishop-de Leeuw theorems
On the convergence of operators
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 powers of Voiculescu's circular element
The main result of the paper is that for a circular element c in a C*-probability space, is an R-diagonal pair in the sense of Nica and Speicher for every n = 1,2,... The coefficients of the R-series are found to be the generalized Catalan numbers of parameter n-1.
On two quantum versions of the detailed balance condition
Quantum detailed balance conditions are often formulated as relationships between the generator of a quantum Markov semigroup and the generator of a dual semigroup with respect to a certain scalar product defined by an invariant state. In this paper we survey some results describing the structure of norm continuous quantum Markov semigroups on ℬ(h) satisfying a quantum detailed balance condition when the duality is defined by means of pre-scalar products on ℬ(h) of the form (s ∈ [0,1]) in order...
On weak convergence of iterates in quantum -spaces .
Operators from C*-algebras to Banach Spaces.