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Fremlin tensor products of concavifications of Banach lattices

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Abstract

Suppose that \(E\) is a uniformly complete vector lattice and \(p_1,\dots ,p_n\) are positive reals. We prove that the diagonal of the Fremlin projective tensor product of \(E_{(p_1)},\dots ,E_{(p_n)}\) can be identified with \(E_{(p)}\) where \(p=p_1+\dots +p_n\) and \(E_{(p)}\) stands for the \(p\)-concavification of \(E\). We also provide a variant of this result for Banach lattices. This extends the main result of Bu et al. (Positivity, 2013).

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Vladimir G. Troitsky

  2. Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran

    Omid Zabeti

Authors
  1. Vladimir G. Troitsky
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  2. Omid Zabeti
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Corresponding author

Correspondence to Vladimir G. Troitsky.

Additional information

The first author was supported by NSERC. The second author was supported by a grant from the Ministry of Science of Iran.

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Troitsky, V.G., Zabeti, O. Fremlin tensor products of concavifications of Banach lattices. Positivity 18, 191–200 (2014). https://doi.org/10.1007/s11117-013-0239-3

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  • DOI: https://doi.org/10.1007/s11117-013-0239-3

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