Rough and strongly rough norms on Banach spaces

Godini, G.

doi:10.1090/S0002-9939-1983-0681828-X

Rough and strongly rough norms on Banach spaces
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Proc. Amer. Math. Soc. 87 (1983), 239-245 Request permission

Abstract:

We give equivalent conditions for a norm on a Banach space $X$ to be rough using the sets $A(x)$ defined for each $x \in X$ by $A(x) = \{ {f \in {X^ * }|f(x) = || x ||,|| f || = 1\}}$. This enables us to obtain unitary characterizations for rough and strongly rough norms.

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Rough and strongly rough norms on Banach spaces