We continue the investigation of the behaviour of diameter two properties in tensor products of Banach spaces. Our main result shows that the symmetric strong diameter two property is stable by taking projective tensor products. We also prove a result for the symmetric strong diameter two property for the injective tensor product.

中文翻译：

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Banach空间张量积的对称强径二性质

我们继续研究 Banach 空间张量积中直径两个属性的行为。我们的主要结果表明，通过采用投影张量积，对称强径二性质是稳定的。我们还证明了注射张量积的对称强直径二性质的结果。