Displaying similar documents to “An inequality between the James and James type constants in Banach spaces”

On the geometry of Banach spaces with modulus of convexity of power type 2

M. Ivanov, A. J. Pallares, S. Troyanski (2010)

Studia Mathematica

Similarity:

We use one-dimensional differential inequalities to estimate the squareness and type of Banach spaces with modulus of convexity of power type two. The estimates obtained are sharp and the constants involved moderate.

Convexity around the Unit of a Banach Algebra

Kadets, Vladimir, Katkova, Olga, Martín, Miguel, Vishnyakova, Anna (2008)

Serdica Mathematical Journal

Similarity:

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.