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Characterizations of weakly compact sets and new fixed point free maps in c₀

P. N. Dowling, C. J. Lennard, B. Turett (2003)

Studia Mathematica

We give a basic sequence characterization of relative weak compactness in c₀ and we construct new examples of closed, bounded, convex subsets of c₀ failing the fixed point property for nonexpansive self-maps. Combining these results, we derive the following characterization of weak compactness for closed, bounded, convex subsets C of c₀: such a C is weakly compact if and only if all of its closed, convex, nonempty subsets have the fixed point property for nonexpansive mappings.

Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections

M. Wojciechowski (1993)

Studia Mathematica

We characterize those anisotropic Sobolev spaces on tori in the L 1 and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author’s earlier paper [W].

Chebyshev centers in hyperplanes of c 0

Libor Veselý (2002)

Czechoslovak Mathematical Journal

We give a full characterization of the closed one-codimensional subspaces of c 0 , in which every bounded set has a Chebyshev center. It turns out that one can consider equivalently only finite sets (even only three-point sets) in our case, but not in general. Such hyperplanes are exactly those which are either proximinal or norm-one complemented.

Chebyshev coficients for L1-preduals and for spaces with the extension property.

José Manuel Bayod Bayod, María Concepción Masa Noceda (1990)

Publicacions Matemàtiques

We apply the Chebyshev coefficients λf and λb, recently introduced by the authors, to obtain some results related to certain geometric properties of Banach spaces. We prove that a real normed space E is an L1-predual if and only if λf(E) = 1/2, and that if a (real or complex) normed space E is a P1 space, then λb(E) equals λb(K), where K is the ground field of E.

Chevet type inequality and norms of submatrices

Radosław Adamczak, Rafał Latała, Alexander E. Litvak, Alain Pajor, Nicole Tomczak-Jaegermann (2012)

Studia Mathematica

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of the expectation of the supremum of “symmetric exponential” processes, compared to the Gaussian ones in the Chevet inequality. This is used to give a sharp upper estimate for a quantity Γ k , m that controls uniformly the Euclidean operator norm of the submatrices with k rows and m columns of an isotropic log-concave unconditional random matrix. We apply these estimates...

Circumcenters in real normed spaces

M. S. Tomás (2005)

Bollettino dell'Unione Matematica Italiana

The study of circumcenters in different types of triangles in real normed spaces gives new characterizations of inner product spaces.

C(K) spaces which cannot be uniformly embedded into c₀(Γ)

Jan Pelant, Petr Holický, Ondřej F. K. Kalenda (2006)

Fundamenta Mathematicae

We give two examples of scattered compact spaces K such that C(K) is not uniformly homeomorphic to any subset of c₀(Γ) for any set Γ. The first one is [0,ω₁] and hence it has the smallest possible cardinality, the other one has the smallest possible height ω₀ + 1.

Clarkson type inequalities and their relations to the concepts of type and cotype.

Mikio Kato, Lars-Erik. Persson, Yasuji Takahashi (2000)

Collectanea Mathematica

We prove some multi-dimensional Clarkson type inequalities for Banach spaces. The exact relations between such inequalities and the concepts of type and cotype are shown, which gives a conclusion in an extended setting to M. Milman's observation on Clarkson's inequalities and type. A similar investigation conceming the close connection between random Clarkson inequality and the corresponding concepts of type and cotype is also included. The obtained results complement, unify and generalize several...

Classical boundary value problems for integrable temperatures in a C 1 domain

Anna Grimaldi Piro, Francesco Ragnedda (1991)

Annales Polonici Mathematici

Abstract. We study a Neumann problem for the heat equation in a cylindrical domain with C 1 -base and data in h c 1 , a subspace of L 1. We derive our results, considering the action of an adjoint operator on B T M O C , a predual of h c 1 , and using known properties of this last space.

Closed operator ideals and limiting real interpolation

Luz M. Fernández-Cabrera, Antón Martínez (2014)

Studia Mathematica

We establish interpolation properties under limiting real methods for a class of closed ideals including weakly compact operators, Banach-Saks operators, Rosenthal operators and Asplund operators. We show that they behave much better than compact operators.

Closed subgroups in Banach spaces

Fredric Ancel, Tadeusz Dobrowolski, Janusz Grabowski (1994)

Studia Mathematica

We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of c 0 . Other results on subgroups of linear spaces are obtained.

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