On Positive Injective Tensor Products Being Grothendieck Spaces

Shaoyong Zhang (), Zhaohui Gu () and Yongjin Li ()
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Shaoyong Zhang: Harbin University of Science and Technology
Zhaohui Gu: Guangdong University of Foreign Studies
Yongjin Li: Sun Yat-sen University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 1239-1246

Abstract: Abstract Let λ be a reflexive Banach sequence lattice and X be a Banach lattice. In this paper, we show that the positive injective tensor product $$\lambda {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over \otimes } _{\left| \varepsilon \right|}}X$$ λ ⊗ ⌣ | ε | X is a Grothendieck space if and only if X is a Grothendieck space and every positive linear operator from λ* to X** is compact.

Keywords: Banach lattice; injective tensor product; Grothendieck spaces; 46B20; 46B28 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0461-1

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