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Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation $U^{}$ 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 $L_{2}$ -spaces

Ferenc Móricz, Barthélemy Le Gac (2000)

Studia Mathematica

The notion of bundle convergence in von Neumann algebras and their $L_{2}$ -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

Silviu Teleman (1982)

Banach Center Publications

On the convergence of operators

Beáta Stehlíková (1988)

Mathematica Slovaca

On the Lebesgue decomposition of Gleason measures

Vladimír Palko (1987)

Časopis pro pěstování matematiky

On the Lebesgue decomposition of the normal states of a JBW-algebra

Jacques Dubois, Brahim Hadjou (1992)

Mathematica Bohemica

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

Ferenc Oravecz (2001)

Studia Mathematica

The main result of the paper is that for a circular element c in a C*-probability space, $(c ⁿ, c^{n *})$ 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

Franco Fagnola, Veronica Umanità (2010)

Banach Center Publications

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 $⟨ x, y ⟩_{s} : = t r (ρ^{1 - s} x * ρ^{s} y)$ (s ∈ [0,1]) in order...

On weak convergence of iterates in quantum $L_{p}$ -spaces $(p \geq 1)$ .

Grabarnik, Genady Ya., Katz, Alexander A., Shwartz, Laura (2005)

International Journal of Mathematics and Mathematical Sciences

Operators from C*-algebras to Banach Spaces.

J.D. Maitland Wright (1980)

Mathematische Zeitschrift

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