基本张量集合在射影张量积中是弱闭合的

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-05-13 DOI:10.1017/s0004972724000376

COLIN PETITJEAN

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引用次数: 0

摘要

我们证明了基本张量集合在两个巴拿赫空间的射影张量积中是弱封闭的。因此，我们回答了罗德里格斯（Rodríguez）和鲁埃达-佐卡（Rueda Zoca）的一个问题['射影张量积中的弱前封闭性'，Indag.(N.S.)35(1) (2024), 60-75)]，证明如果 $(x_n) \subset X$ 和 $(y_n) \subset Y$ 是两个弱空序列，使得 $(x_n \otimes y_n)$ 在 $X \widehat {\otimes }_\pi Y$ 中弱收敛，那么 $(x_n \otimes y_n)$ 也是弱空的。

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THE SET OF ELEMENTARY TENSORS IS WEAKLY CLOSED IN PROJECTIVE TENSOR PRODUCTS

We prove that the set of elementary tensors is weakly closed in the projective tensor product of two Banach spaces. As a result, we answer a question of Rodríguez and Rueda Zoca [‘Weak precompactness in projective tensor products’, Indag. Math. (N.S.)35(1) (2024), 60–75], proving that if

$(x_n) \subset X$

and

$(y_n) \subset Y$

are two weakly null sequences such that

$(x_n \otimes y_n)$

converges weakly in

$X \widehat {\otimes }_\pi Y$

, then

$(x_n \otimes y_n)$

is also weakly null.

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society