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Tensor product construction of 2-freeness

R. Lenczewski (1998)

Banach Center Publications

From a sequence of m-fold tensor product constructions that give a hierarchy of freeness indexed by natural numbers m we examine in detail the first non-trivial case corresponding to m=2 which we call 2-freeness. We show that in this case the constructed tensor product of states agrees with the conditionally free product for correlations of order ≤ 4. We also show how to associate with 2-freeness a cocommutative *-bialgebra.

Tensor products of Hilbert modules over locally C * -algebras

Maria Joiţa (2004)

Czechoslovak Mathematical Journal

In this paper the tensor products of Hilbert modules over locally C * -algebras are defined and their properties are studied. Thus we show that most of the basic properties of the tensor products of Hilbert C * -modules are also valid in the context of Hilbert modules over locally C * -algebras.

The alternative Dunford-Pettis Property in the predual of a von Neumann algebra

Miguel Martín, Antonio M. Peralta (2001)

Studia Mathematica

Let A be a type II von Neumann algebra with predual A⁎. We prove that A⁎ does not have the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φₙ) converging weakly to φ in A⁎ with ||φₙ|| = ||φ|| = 1 for all n ∈ ℕ and a weakly null sequence (xₙ) in A such that φₙ(xₙ) ↛ 0. This answers a question posed in [7].

The arithmetic of distributions in free probability theory

Gennadii Chistyakov, Friedrich Götze (2011)

Open Mathematics

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 C * -algebra of a Hilbert bimodule

Sergio Doplicher, Claudia Pinzari, Rita Zuccante (1998)

Bollettino dell'Unione Matematica Italiana

Un C * -modulo hilbertiano destro X su una C * -algebra A dotato di uno * -omomorfismo isometrico ϕ : A L A X viene qui considerato come un oggetto X A della C * -categoria degli A -moduli Hilbertiani destri. Come in [11], associamo ad esso una C * -algebra O X A contenente X come un « A -bimodulo hilbertiano in O X A ». Se X è pieno e proiettivo finito O X A è la C * -algebra C * X , la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, C * X è canonicamente immersa...

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