Fremlin tensor products of concavifications of Banach lattices

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• 作者：Vladimir G. Troitsky (1)
  Omid Zabeti (2)
  
• 关键词：Vector lattice ; Banach lattice ; Fremlin projective tensor product ; Diagonal of tensor product ; Concavification ; Primary 46B42 ; Secondary 46M05 ; 46B40 ; 46B45
• 刊名：Positivity
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：18
• 期：1
• 页码：191-200
• 全文大小：241 KB
• 作者单位：Vladimir G. Troitsky (1)
  Omid Zabeti (2)
  
  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
  2. Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran
  
• ISSN：1572-9281

文摘

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).