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.
Banach J. Math. Anal.
10(4):
771-782
(October 2016).
DOI: 10.1215/17358787-3649392