AI 中文总结
该研究针对巴拿赫格张量积，建立了Cembranos定理的正类似结论，给出Wittstock张量积含$c_0$补副本、不具备正Grothendieck性质的条件，推进了巴拿赫格正张量积结构的研究。
AI 中文摘要
Cembranos的一个结果指出，C-空间的非平凡内射张量积包含一个$c_{0}$的补副本，尤其不具备Grothendieck性质。我们针对巴拿赫格的张量积建立了Cembranos定理的正类似结论。若E和F为无限维巴拿赫格，且E包含$c_{0}$，同时$E^{\text{*}}$或$F^{\text{*}}$具有有界正逼近性质，则Wittstock张量积$E\tilde{\boxtimes}_{|\boldsymbol{\text{ε}}|}F$包含一个$c_{0}$的补副本。若F还具有自反性，则$E\tilde{\boxtimes}_{|\boldsymbol{\text{ε}}|}F$不具备正Grothendieck性质。
英文摘要
A result of Cembranos states that a non-trivial injective tensor product of a $C$-space contains a complemented copy of $c_{0}$, and in particular fails the Grothendieck property. We establish a positive analogue of the Cembranos theorem for tensor products of Banach lattices. If $E$ and $F$ are infinite dimensional Banach lattices, with $E$ containing $c_{0}$ and $E^{\ast}$ or $F^{\ast}$ having the bounded positive approximation property, then the Wittstock tensor product $E\widetilde{\otimes}_{\vert{\varepsilon}\vert}F$ contains a complemented copy of $c_{0}$. If $F$ is in addition reflexive, then $E\widetilde{\otimes}_{\vert{\varepsilon}\vert}F$ fails the positive Grothendieck property.
