On convexity and smoothness of Banach space
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Commentationes Mathematicae Universitatis Carolinae
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Displaying similar documents to “On the geometry of Banach spaces with modulus of convexity of power type 2”
On convexity and smoothness of Banach space
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2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12. We estimate the (midpoint) modulus of convexity at the unit 1 of a Banach algebra A showing that inf {max±||1 ± x|| − 1 : x ∈ A, ||x||=ε} ≥ (π/4e)ε²+o(ε²) as ε → 0. We also give a characterization of two-dimensional subspaces of Banach algebras containing the identity in terms of polynomial inequalities.
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