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A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces

G. Androulakis (1998)

Studia Mathematica

Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and there exists...

A survey on topological games and their applications in analysis.

Jiling Cao, Warren B. Moors (2006)

RACSAM

In this survey article we shall summarise some of the recent progress that has occurred in the study of topological games as well as their applications to abstract analysis. The topics given here do not necessarily represent the most important problems from the area of topological games, but rather, they represent a selection of problems that are of interest to the authors.

A theorem on isotropic spaces

Félix Cabello Sánchez (1999)

Studia Mathematica

Let X be a normed space and G F ( X ) the group of all linear surjective isometries of X that are finite-dimensional perturbations of the identity. We prove that if G F ( X ) acts transitively on the unit sphere then X must be an inner product space.

A universal modulus for normed spaces

Carlos Benítez, Krzysztof Przesławski, David Yost (1998)

Studia Mathematica

We define a handy new modulus for normed spaces. More precisely, given any normed space X, we define in a canonical way a function ξ:[0,1)→ ℝ which depends only on the two-dimensional subspaces of X. We show that this function is strictly increasing and convex, and that its behaviour is intimately connected with the geometry of X. In particular, ξ tells us whether or not X is uniformly smooth, uniformly convex, uniformly non-square or an inner product space.

About some parameters of normed linear spaces

Emanuele Casini (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si prendono in considerazione particolari costanti relative alla struttura della sfera unitaria di uno spazio di Banach. Se ne studiano alcune generali proprietà, con particolare riferimento alle relazioni con il modulo di convessità dello spazio. Se ne fornisce inoltre una esatta valutazione negli spazi l p .

Almost ball remotal subspaces in Banach spaces

Tanmoy Paul (2012)

Studia Mathematica

We investigate almost ball remotal and ball remotal subspaces of Banach spaces. Several subspaces of the classical Banach spaces are identified having these properties. Some stability results for these properties are also proved.

An alternative Dunford-Pettis Property

Walden Freedman (1997)

Studia Mathematica

An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that ℓ p -direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.

An alternative polynomial Daugavet property

Elisa R. Santos (2014)

Studia Mathematica

We introduce a weaker version of the polynomial Daugavet property: a Banach space X has the alternative polynomial Daugavet property (APDP) if every weakly compact polynomial P: X → X satisfies m a x ω ∈ | | I d + ω P | | = 1 + | | P | | . We study the stability of the APDP by c₀-, ℓ ∞ - and ℓ₁-sums of Banach spaces. As a consequence, we obtain examples of Banach spaces with the APDP, namely L ∞ ( μ , X ) and C(K,X), where X has the APDP.

An alternative proof of Petty's theorem on equilateral sets

Tomasz Kobos (2013)

Annales Polonici Mathematici

The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth point,...

Currently displaying 61 – 80 of 113