Banach格的正张量积的序连续

张少勇, 刘琪, 黎永锦

数学学报 ›› 2021, Vol. 64 ›› Issue (3) : 405-412.

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PDF(344 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (3) : 405-412. DOI: 10.12386/A2021sxxb0034
论文

Banach格的正张量积的序连续

    张少勇1, 刘琪2, 黎永锦2
作者信息 +

Order Continuity of Positive Tensor Products of Banach Lattices

    Shao Yong ZHANG1, Qi LIU2, Yong Jin LI2
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摘要

对于Banach序列格λ和Banach格Xλ|π| X(或λ|ε| X)表示λX的正投影(或射影)张量积.本文证明了:如果λσ-Levi空间,那么λ|π| X(或λ|ε| X)是序或σ-序连续的当且仅当λX都是序或σ-序连续的.同样证明了:如果λσ-序连续的,那么λ|π| X是Levi或σ-Levi空间当且仅当λX都是Levi或σ-Levi空间.

Abstract

For a Banach sequence lattice λ and a Banach lattice X, let λ|π| X (resp. λ|ε| X) denote the positive projective (resp. injective) tensor product of λ and X. In the paper we prove that if λ is a σ-Levi space then λ|π| X (resp. λ|ε| X) is order or σ-order continuous if and only if both λ and X are order or σ-order continuous. We also prove that if λ is σ-order continuous then λ|π| X is a Levi or σ-Levi space if and only if both λ and X are Levi or σ-Levi spaces.

关键词

正张量积 / Banach格 / 序连续 / Levi空间

Key words

positive tensor product / Banach lattice / order continuity / Levi space

引用本文

导出引用
张少勇, 刘琪, 黎永锦. Banach格的正张量积的序连续. 数学学报, 2021, 64(3): 405-412 https://doi.org/10.12386/A2021sxxb0034
Shao Yong ZHANG, Qi LIU, Yong Jin LI. Order Continuity of Positive Tensor Products of Banach Lattices. Acta Mathematica Sinica, Chinese Series, 2021, 64(3): 405-412 https://doi.org/10.12386/A2021sxxb0034

参考文献

[1] Bu Q. Y., Buskes G., Schauder decompositions and the Fremlin projective tensor product of Banach lattices, J. Math. Anal. Appl., 2009, 355:335-351.
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[3] Bu Q. Y., Wong N. C., Some geometric properties inherited by the positive tensor products of atomic Banach lattices, Indag. Math. (N.S.), 2012, 23:199-213.
[4] Fremlin D. H., Tensor products of Archimedean vector lattices, Amer. J. Math., 1972, 94:778-798.
[5] Fremlin D. H., Tensor products of Banach lattices, Math. Ann., 1974, 211:87-106.
[6] Meyer-Nieberg P., Banach Lattices, Springer-Verlag, Berlin, 1991.
[7] Wittstock G., Eine Bemerkung über Tensorprodukte von Banachverbänden, Arch. Math., 1974, 25:627-634.
[8] Wittstock G., Ordered Normed Tensor Products, In:Foundations of Quantum Mechanics and Ordered Linear Spaces, Lecture Notes in Physics, Vol. 29, pp. 67-84. Springer, Berlin, 1974.

基金

国家自然科学基金资助项目(11971493);黑龙江省自然科学基金项目(A2018006)
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