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 \(\lambda {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over \otimes } _{\left| \varepsilon \right|}}X\) is a Grothendieck space if and only if X is a Grothendieck space and every positive linear operator from λ* to X** is compact.

中文翻译：

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关于正射量张量积为Grothendieck空间

令λ为自反Banach序列晶格，X为Banach晶格。在本文中，我们证明了正射量张量积\（\ lambda {\ mathord {\ buildrel {\ lower3pt \ hbox {$ \ scriptscriptstyle \ smile $}} \ over \ otimes} _ {\ left | \ varepsilon \ right |}} X \）是Grothendieck空间，并且仅当X是Grothendieck空间并且从λ *到X **的每个正线性算子都是紧凑的。