All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 38 Next

Displaying 741 – 760 of 880

Showing per page

Convex sets in Banach spaces and a problem of Rolewicz

A. Granero, M. Jiménez Sevilla, J. Moreno (1998)

Studia Mathematica

Let B x be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of B x and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).

Convex transformations with Banach lattice range.

Roman Ger (1987)

Stochastica

A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised by Ih-Ching...

Convex-compact sets and Banach discs

I. Monterde, Vicente Montesinos (2009)

Czechoslovak Mathematical Journal

Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual E ' of a locally convex space E is the σ ( E ' , E ) -closure of the union of countably many σ ( E ' , E ) -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.

Convexity around the Unit of a Banach Algebra

Kadets, Vladimir, Katkova, Olga, Martín, Miguel, Vishnyakova, Anna (2008)

Serdica Mathematical Journal

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.

Convex-like inequality, homogeneity, subadditivity, and a characterization of L p -norm

Janusz Matkowski, Marek Pycia (1995)

Annales Polonici Mathematici

Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that l i m s u p t → 0 + f ( t ) ≤ 0 must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the L p -norm.

Convolution algebras with weighted rearrangement-invariant norm

R. Kerman, E. Sawyer (1994)

Studia Mathematica

Let X be a rearrangement-invariant space of Lebesgue-measurable functions on ℝ n , such as the classical Lebesgue, Lorentz or Orlicz spaces. Given a nonnegative, measurable (weight) function on ℝ n , define X ( w ) = F : ℝ n → ℂ : ∞ > ∥ F ∥ X ( w ) : = ∥ F w ∥ X . We investigate conditions on such a weight w that guarantee X(w) is an algebra under the convolution product F∗G defined at x ∈ ℝ n by ( F ∗ G ) ( x ) = ʃ ℝ n F ( x - y ) G ( y ) d y ; more precisely, when ∥ F ∗ G ∥ X ( w ) ≤ ∥ F ∥ X ( w ) ∥ G ∥ X ( w ) for all F,G ∈ X(w).

Currently displaying 741 – 760 of 880