Rough and strongly rough norms on Banach spaces
G. Godini · Proceedings of the American Mathematical Society · 1983
We give equivalent conditions for a norm on a Banach space X X to be rough using the sets A ( x ) A(x) defined for each x ∈ X x \in X by A ( x ) = { f ∈ X ∗ | f ( x ) = | | x | | , | | f | | = 1 } A(x) = \{ {f \in {X^ * }|f(x) = || x ||,|| f || = 1\}} . This enables us to obtain unitary characterizations for rough and strongly rough norms.