We study when diameter properties can be inherited by subspaces. We obtain that the slice diameter property (resp., the diameter property, strong diameter property) passes from a Banach space to a subspace whenever is finite-dimensional and is complemented by a norm projection (resp., the quotient is finite-dimensional and strongly regular). Also, we study the same problem for the dual properties of diameter properties, such as having octahedral, weakly octahedral, or -rough norm.
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