Convexity around the Unit of a Banach Algebra

Kadets, Vladimir, et al. "Convexity around the Unit of a Banach Algebra." Serdica Mathematical Journal 34.3 (2008): 619-628. <http://eudml.org/doc/281446>.

@article{Kadets2008,
abstract = {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.},
author = {Kadets, Vladimir, Katkova, Olga, Martín, Miguel, Vishnyakova, Anna},
journal = {Serdica Mathematical Journal},
keywords = {Unital Banach Algebra; Strongly Extreme Point; Midpoint Modulus of Local Convexity; unital Banach algebra; strongly extreme point; midpoint modulus of local convexity},
language = {eng},
number = {3},
pages = {619-628},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Convexity around the Unit of a Banach Algebra},
url = {http://eudml.org/doc/281446},
volume = {34},
year = {2008},
}

TY - JOUR
AU - Kadets, Vladimir
AU - Katkova, Olga
AU - Martín, Miguel
AU - Vishnyakova, Anna
TI - Convexity around the Unit of a Banach Algebra
JO - Serdica Mathematical Journal
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 3
SP - 619
EP - 628
AB - 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.
LA - eng
KW - Unital Banach Algebra; Strongly Extreme Point; Midpoint Modulus of Local Convexity; unital Banach algebra; strongly extreme point; midpoint modulus of local convexity
UR - http://eudml.org/doc/281446
ER -