Fremlin tensor products of concavifications of Banach lattices

被引：4
|
作者：
Troitsky, Vladimir G. [1 ]
Zabeti, Omid [2 ]
机构：
[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
[2] Univ Sistan & Baluchestan, Fac Math, Dept Math, Zahedan, Iran
来源：
POSITIVITY | 2014年 / 18卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Vector lattice; Banach lattice; Fremlin projective tensor product; Diagonal of tensor product; Concavification; F-ALGEBRAS;
D O I：
10.1007/s11117-013-0239-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Suppose that is a uniformly complete vector lattice and are positive reals. We prove that the diagonal of the Fremlin projective tensor product of can be identified with where and stands for the -concavification of . We also provide a variant of this result for Banach lattices. This extends the main result of Bu et al. (Positivity, 2013).
引用
收藏
页码：191 / 200
页数：10
相关论文
共 50 条
  • [21] The Radon-Nikodym Property for Tensor Products of Banach Lattices II
    Qingying Bu
    Gerard Buskes
    Wei-Kai Lai
    [J]. Positivity, 2008, 12 : 45 - 54
  • [22] Joint continuity of injective tensor products of vector measures in Banach lattices
    Kawabe, J
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2003, 74 : 185 - 199
  • [23] A topology on the Fremlin tensor product of locally convex-solid vector lattices
    Zabeti, Omid
    [J]. ARCHIV DER MATHEMATIK, 2024,
  • [24] Banach Lattice Structures and Concavifications in Banach Spaces
    Agud, Lucia
    Calabuig, Jose Manuel
    Juan, Maria Aranzazu
    Sanchez Perez, Enrique A.
    [J]. MATHEMATICS, 2020, 8 (01)
  • [25] Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I
    Donghai Ji
    Michelle Craddock
    Qingying Bu
    [J]. Positivity, 2010, 14 : 59 - 68
  • [26] REFLEXIVITY AND THE GROTHENDIECK PROPERTY FOR POSITIVE TENSOR PRODUCTS OF BANACH LATTICES-II
    Bu, Qingying
    Craddock, Michelle
    Ji, Donghai
    [J]. QUAESTIONES MATHEMATICAE, 2009, 32 (03) : 339 - 350
  • [27] Reflexivity and the Grothendieck property for positive tensor products of Banach lattices-I
    Ji, Donghai
    Craddock, Michelle
    Bu, Qingying
    [J]. POSITIVITY, 2010, 14 (01) : 59 - 68
  • [28] Some geometric properties inherited by the positive tensor products of atomic Banach lattices
    Bu, Qingying
    Wong, Ngai-Ching
    [J]. INDAGATIONES MATHEMATICAE-NEW SERIES, 2012, 23 (03): : 199 - 213
  • [29] The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square
    Bu, Qingying
    Buskes, Gerard
    Popov, Alexey I.
    Tcaciuc, Adi
    Troitsky, Vladimir G.
    [J]. POSITIVITY, 2013, 17 (02) : 283 - 298
  • [30] The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square
    Qingying Bu
    Gerard Buskes
    Alexey I. Popov
    Adi Tcaciuc
    Vladimir G. Troitsky
    [J]. Positivity, 2013, 17 : 283 - 298
12345