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

• Autorzy: Miguel Martín , Antonio M. Peralta
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 46L10: General theory of von Neumann algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 2
• Strony: 197-200

Daty

wydano

2001

Twórcy

autor

Miguel Martín

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

autor

Antonio M. Peralta

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm147-2-7