STRICT CONVEXITY THROUGH EQUIVALENT NORMS IN SEPARABLES BANACH SPACES
DOI:
https://doi.org/10.17268/sel.mat.2016.02.06Keywords:
Strict convexity, dual norm, separable Banach spacesAbstract
Let E be a separable Banach space with norm || . ||. In the present work, the objective is to construct a norm || . ||1 that is equivalent to || . || in E, such that || . ||1 is strictly convex. In addition it is shown that its dual conjugate norm is also strictly convex.
References
H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer Science -Business Media, LLC 2011.
G. Botelho, D. Pellegrino and E. Teixeira. Fundamentos de Analise Funcional, EditorasBM, Brasil, 2012.
F. Alvarez. Análisis Convexo y Dualidad, DIM-CMM, Universidad de Chile, 2012.
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