对于Banach序列格λ和Banach格X,λ⊗|π| X(或λ⊗|ε| X)表示λ和X的正投影(或射影)张量积.本文证明了:如果λ是σ-Levi空间,那么λ⊗|π| X(或λ⊗|ε| X)是序或σ-序连续的当且仅当λ和X都是序或σ-序连续的.同样证明了:如果λ是σ-序连续的,那么λ⊗|π| X是Levi或σ-Levi空间当且仅当λ和X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
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Key words
positive tensor product /
Banach lattice /
order continuity /
Levi space
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参考文献
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脚注
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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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