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The n -dual space of the space of p -summable sequences

Yosafat E. P. Pangalela, Hendra Gunawan (2013)

Mathematica Bohemica

In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an n -normed space, we are interested in bounded multilinear n -functionals and n -dual spaces. The concept of bounded multilinear n -functionals on an n -normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear n -functionals, introduce the concept of n -dual spaces, and...

The Space of Differences of Convex Functions on [0, 1]

Zippin, M. (2000)

Serdica Mathematical Journal

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1]

Triebel-Lizorkin spaces with non-doubling measures

Yongsheng Han, Dachun Yang (2004)

Studia Mathematica

Suppose that μ is a Radon measure on ℝ d , which may be non-doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀ > 0 such that for all x ∈ supp(μ) and r > 0, μ(B(x,r)) ≤ C₀rⁿ, where 0 < n ≤ d. The authors provide a theory of Triebel-Lizorkin spaces Ḟ p q s ( μ ) for 1 < p < ∞, 1 ≤ q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure μ, C₀, n and d. The method does not use the vector-valued maximal function inequality...

Two geometric constants for operators acting on a separable Banach space.

E. Martín Peinador, E. Induráin, A. Plans Sanz de Bremond, A. A. Rodes Usan (1988)

Revista Matemática de la Universidad Complutense de Madrid

The main result of this paper is the following: A separable Banach space X is reflexive if and only if the infimum of the Gelfand numbers of any bounded linear operator defined on X can be computed by means of just one sequence on nested, closed, finite codimensional subspaces with null intersection.

Une nouvelle classe d'espaces de Banach vérifiant le théorème de Grothendieck

Gilles Pisier (1978)

Annales de l'institut Fourier

Soit W un espace ℒ 1 et soit R un sous-espace réflexif de dimension infinie de W . Nous montrons que le quotient W / R vérifie le théorème de Grothendieck, c’est-à-dire que tout opérateur de W / R dans un espace de Hilbert est 1-sommant; par ailleurs, W / R n’est pas un espace ℒ 1 . Cela permet de répondre négativement à une question de Lindenstrauss-Pełczyński ainsi qu’à une question similaire de Grothendieck.

Currently displaying 281 – 300 of 336