Unital Banach Algebra Strongly Extreme Point Midpoint Modulus of Local Convexity
Issue Date:
2008
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 34, No 3, (2008), 619p-628p
Abstract:
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.
