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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 $C^{*}$ -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 $ϕ : A \to L_{A} (X)$ 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...

Currently displaying 1 – 20 of 53

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Displaying 1 – 20 of 53

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

The $C^{*}$ -algebra of a Hilbert bimodule

The $C^{*}$ -algebras of row-finite graphs.

The C*-algebra generated by two projections.

The C*-Algebra of a Singular Elliptic Problem on a Noncompact Riemannian Manifold.

The correspondence associated to an inner completely positive map.

The dual of the multiplier algebra of Pedersen's ideal.

The Dunford-Pettis property in C*-algebras

The elements of bounded trace in the C*-algebra of a nilpotent Lie group.

The Exponential Rank of Inductive Limit C*-Algebras.

The Facial Q-Topology for Compact Convex Sets.

The General Stone-Weierstrass Problem and Extremal Completely Positive Maps.

The graph traces of finite graphs and applications to tracial states of $C^{*}$ -algebras.

The group of invertible elements in a Banach algebra

The Hilbert projective metric and an equation in a $C^{*}$ -algebra

The ideal structure of the Haagerup tensor product of C*-algebras.

The isolated ideal of a correspondence associated with a topological quiver.

The joint approximate spectrum of a finite system of elements of a C*-algebra

The Lie structure of C* and Poisson algebras

The Linear Groups of Injective Factors and of Matroid C*Algebras are Contractible to a Point.

Currently displaying 1 – 20 of 53