Convex sets and Harnack inequality
Convex sets in Banach spaces and a problem of Rolewicz
Let 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 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 Trace Functions and the Wigner-Yanase-Dyson Conjecture
Convex transformations with Banach lattice range.
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
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 of a locally convex space is the -closure of the union of countably many -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.
Convexification of conjugate functions.
Convexités dans les espaces vectoriels topologiques généraux [Book]
Convexités uniformes et inégalités de martingales.
Convexity and Reflexivity
Convexity around the Unit of a Banach Algebra
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.
Convexity conditions in normed linear spaces.
Convexity in combinatorial structures
Convexity in complex analysis
Convexity of measures in certain convex cones in vector space ...-algebras.
Convexity on a topological space
Convexity preserving summability matrices.
Convexity, type and three space problem
Convex-like inequality, homogeneity, subadditivity, and a characterization of -norm
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 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 -norm.
Convolution algebras with weighted rearrangement-invariant norm
Let X be a rearrangement-invariant space of Lebesgue-measurable functions on , such as the classical Lebesgue, Lorentz or Orlicz spaces. Given a nonnegative, measurable (weight) function on , define . We investigate conditions on such a weight w that guarantee X(w) is an algebra under the convolution product F∗G defined at by ; more precisely, when for all F,G ∈ X(w).
Convolution and S' - Convolution of Distributions