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Title: Convexity around the Unit of a Banach Algebra
Authors: Kadets, Vladimir
Katkova, Olga
Martín, Miguel
Vishnyakova, Anna
Keywords: 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.
Description: 2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 3

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