Stability of diametral diameter two properties

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