We prove that the diametral diameter two properties are inherited by F-ideals (e.g., M-ideals). On the other hand, these properties are lifted from an M-ideal to the superspace under strong geometric assumptions. We also show that all of the diametral diameter two properties are stable under the formation of corresponding Köthe–Bochner spaces (e.g., \(L_p\)-Bochner spaces). Finally, we investigate when the projective tensor product of two Banach spaces has some diametral diameter two property.

中文翻译：

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直径直径稳定性两个特性

我们证明直径直径的两个属性是F- ideals（例如M- ideals）所继承的。另一方面，在强几何假设下，这些性质从M理想提升到超空间。我们还表明，在相应的Köthe–Bochner空间（例如\（L_p \） -Bochner空间）的形成下，所有直径直径的两个属性都是稳定的。最后，我们研究了两个Banach空间的射影张量积具有一定的直径二性质。