A Kadec-Pelczyński dichotomy-type theorem for preduals of JBW*-algebras

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• 作者：Francisco J. Fernández-Polo ; Antonio M. Peralta…
• 刊名：Israel Journal of Mathematics
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：208
• 期：1
• 页码：45-78
• 全文大小：346 KB
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• 作者单位：Francisco J. Fernández-Polo (1)
  Antonio M. Peralta (1)
  María Isabel Ramírez (2)
  
  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain
  2. Departamento de Algebra y Análisis Matemático, Universidad de Almería, 04120, Almería, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511

文摘

We prove a Kadec-Pelczyński dichotomy-type theorem for bounded sequences in the predual of a JBW*-algebra, showing that for each bounded sequence (? _n ) in the predual of a JBW*-algebra M, there exist a subsequence (? _τ(n), and a sequence of mutually orthogonal projections (p _n ) in M such that: (a) the set \(\{ {\phi _{\tau (n)}} - {\phi _{\tau (n)}}{P_2}({p_n}):n \in {\Bbb N}\} \) is relatively weakly compact