On measure for projectors
An example of a finite set of projectors in is exhibited for which no 0-1 measure exists.
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Václav Alda (1980)
Aplikace matematiky
An example of a finite set of projectors in is exhibited for which no 0-1 measure exists.
Václav Alda (1981)
Aplikace matematiky
Florent Benaych-Georges (2010)
Annales de l'I.H.P. Probabilités et statistiques
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.
Kargin, Vladislav (2008)
Electronic Communications in Probability [electronic only]
D. M. Shaydayeva (1984)
Czechoslovak Mathematical Journal
A. Paszkiewicz (1980)
Colloquium Mathematicae
Pavel Stavinoha (1982)
Czechoslovak Mathematical Journal
Anna Dorota Krystek (2010)
Banach Center Publications
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...
Silviu Teleman (1982)
Banach Center Publications
Beáta Stehlíková (1988)
Mathematica Slovaca
Fannes, Mark, Petz, Dénes (2002)
International Journal of Mathematics and Mathematical Sciences
Munteanu, Bogdan Gheorghe (2007)
General Mathematics
Vladimír Palko (1987)
Časopis pro pěstování matematiky
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.
Kamil Szpojankowski (2015)
Studia Mathematica
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.
J.D. Maitland Wright (1980)
Mathematische Zeitschrift
Wojciech Młotkowski (2002)
Studia Mathematica
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.
Lothar M. Schmitt (1987)
Mathematische Zeitschrift
Erwin Neuhardt (1990)
Mathematica Scandinavica
Stanisław Goldstein (1984)
Studia Mathematica
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