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

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Abstract

We prove a Kadec-Pelczyński dichotomy-type theorem for bounded sequences in the predual of a JBW*-algebra, showing that for each bounded sequence (ϕ n ) in the predual of a JBW*-algebra M, there exist a subsequence (ϕ τ(n), and a sequence of mutually orthogonal projections (p n ) in M such that:

  1. (a)

    the set \(\{ {\phi _{\tau (n)}} - {\phi _{\tau (n)}}{P_2}({p_n}):n \in {\Bbb N}\} \) is relatively weakly compact

  2. (b)

    ϕ τ(n) = ξ n + ψ n , with ξ n := ϕ τ(n) − ϕ τ(n) P 2(p n ), and ψ n := ϕ τ(n) P 2(p n ), (ξ n Q(p n ) = 0 and ψ n Q(p n )2 = ψ n ) for every n.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Francisco J. Fernández-Polo & Antonio M. Peralta

  2. Departamento de Algebra y Análisis Matemático, Universidad de Almería, 04120, Almería, Spain

    María Isabel Ramírez

Authors
  1. Francisco J. Fernández-Polo
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  2. Antonio M. Peralta
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  3. María Isabel Ramírez
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Corresponding author

Correspondence to Francisco J. Fernández-Polo.

Additional information

First and second authors partially supported by the Spanish Ministry of Economy and Competitiveness, D.G.I. project no. MTM2011-23843, and Junta de Andalucía grants FQM0199 and FQM3737.

Third author supported partially supported by the Spanish Ministry of Economy and Competitiveness project no. MTM2010-17687.

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Fernández-Polo, F.J., Peralta, A.M. & Ramírez, M.I. A Kadec-Pelczyński dichotomy-type theorem for preduals of JBW*-algebras. Isr. J. Math. 208, 45–78 (2015). https://doi.org/10.1007/s11856-015-1193-5

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  • DOI: https://doi.org/10.1007/s11856-015-1193-5

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