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2002 A NEW PROOF OF $\ell_1\stackrel{\vee}{\bigotimes} X\subseteq c_0\stackrel{\wedge}{\bigotimes}X$
Qingying Bu
Taiwanese J. Math. 6(2): 181-185 (2002). DOI: 10.11650/twjm/1500407428


In this paper, we first show that for any Banach space $X$, $\ell_1[X]\subseteq\ell_\infty\langle X\rangle$ by Khinchin's inequality. Then by the relationship between Banach-valued sequence spaces and tensor products, we show that for any Banach space $X$, $\ell_1\stackrel{\vee}{\otimes}X\subseteq c_0\stackrel{\wedge}{\otimes}X$.


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Qingying Bu. "A NEW PROOF OF $\ell_1\stackrel{\vee}{\bigotimes} X\subseteq c_0\stackrel{\wedge}{\bigotimes}X$." Taiwanese J. Math. 6 (2) 181 - 185, 2002.


Published: 2002
First available in Project Euclid: 18 July 2017

zbMATH: 1019.46014
MathSciNet: MR1903135
Digital Object Identifier: 10.11650/twjm/1500407428

Primary: 46B28
Secondary: 46B45

Keywords: Banach sequence space , Khinchin's inequality , tensor product

Rights: Copyright © 2002 The Mathematical Society of the Republic of China

Vol.6 • No. 2 • 2002
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