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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Rough and strongly rough norms on Banach spaces


Author: G. Godini
Journal: Proc. Amer. Math. Soc. 87 (1983), 239-245
MSC: Primary 46B20
MathSciNet review: 681828
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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^ * }\vert f(x) = \vert\vert x \vert\vert,\vert\vert f \vert\vert = 1\}}$. This enables us to obtain unitary characterizations for rough and strongly rough norms.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0681828-X
Article copyright: © Copyright 1983 American Mathematical Society