# Convexity around the Unit of a Banach Algebra

Kadets, Vladimir; Katkova, Olga; Martín, Miguel; Vishnyakova, Anna

Serdica Mathematical Journal (2008)

- Volume: 34, Issue: 3, page 619-628
- ISSN: 1310-6600

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topKadets, 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 -

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