Two near-isometry invariants of Banach spaces
Robert A. McGuigan, Jr. (1970)
Compositio Mathematica
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Robert A. McGuigan, Jr. (1970)
Compositio Mathematica
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K. Sundaresan (1973)
Studia Mathematica
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M. Cambern (1965)
Studia Mathematica
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A. Tromba (1976)
Studia Mathematica
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Kadets, Vladimir, Katkova, Olga, Martín, Miguel, Vishnyakova, Anna (2008)
Serdica Mathematical Journal
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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.
Ehrhard Behrends, Vladimir M. Kadets (2001)
Studia Mathematica
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A metric space (M,d) is said to have the small ball property (sbp) if for every ε₀ > 0 it is possible to write M as the union of a sequence (B(xₙ,rₙ)) of closed balls such that the rₙ are smaller than ε₀ and lim rₙ = 0. We study permanence properties and examples of sbp. The main results of this paper are the following: 1. Bounded convex closed sets in Banach spaces have sbp only if they are compact. 2. Precisely the finite-dimensional Banach spaces have sbp. (More generally: a complete...
D. Azagra, J. Gómez, J. A. Jaramillo (1996)
Extracta Mathematicae
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T. S. S. R. K. Rao (1997)
Extracta Mathematicae
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Cardwell, Antonia E. (2006)
International Journal of Mathematics and Mathematical Sciences
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J. C. Navarro-Pascual, M. G. Sanchez-Lirola (2009)
Studia Mathematica
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We study the extremal structure of Banach spaces of continuous functions with the diameter norm.
Libor Veselý (1993)
Acta Universitatis Carolinae. Mathematica et Physica
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Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)
Colloquium Mathematicae
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We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X). ...