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On weak* convergent sequences in duals of symmetric spaces of τ-measurable operators

Journal Article (2017)
Author(s)

B. de Pagter (TU Delft - Electrical Engineering, Mathematics and Computer Science)

P.G. Dodds (University of New South Wales)

F.A. Sukochev (University of New South Wales)

Research Group
Analysis
DOI related publication
https://doi.org/10.1007/s11856-017-1585-9 Final published version
More Info
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Publication Year
2017
Language
English
Research Group
Analysis
Issue number
1
Volume number
222
Pages (from-to)
125-164
Downloads counter
211

Abstract

It is shown that the pre-dual of a σ-finite von Neumann algebra has property (k) in the sense of Figiel, Johnson and Pelczyński [12]. This resolves in the affirmative an open question raised in [12]. It is shown further that a weakly sequentially complete symmetric space E of τ-measurable operators affiliated with a semifinite σ-finite von Neumann algebra has property (k).