The maximum distance between two-dimensional Banach spaces.
The maximum path theorem and extreme points of James space
The Mazur intersection property for families of closed bounded convex sets in Banach spaces
The minimal displacement problem in subspaces of the space of continuous functions of finite codimension
We show that every subspace of finite codimension of the space C[0,1] is extremal with respect to the minimal displacement problem.
The Minkowski plane and the geometry of Banach spaces.
The -dual space of the space of -summable sequences
In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an -normed space, we are interested in bounded multilinear -functionals and -dual spaces. The concept of bounded multilinear -functionals on an -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 -functionals, introduce the concept of -dual spaces, and...
The n-ball properties in real and complex Banach spaces.
The numerical radius of Lipschitz operators on Banach spaces
We study the numerical radius of Lipschitz operators on Banach spaces. We give its basic properties. Our main result is a characterization of finite-dimensional real Banach spaces with Lipschitz numerical index 1. We also explicitly compute the Lipschitz numerical index of some classical Banach spaces.
The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of
Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of . Then the Bochner space is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.
The property () of Orlicz-Bochner sequence spaces
A characterization of property of an arbitrary Banach space is given. Next it is proved that the Orlicz-Bochner sequence space has the property if and only if both spaces and have it also. In particular the Lebesgue-Bochner sequence space has the property iff has the property . As a corollary we also obtain a theorem proved directly in [5] which states that in Orlicz sequence spaces equipped with the Luxemburg norm the property , nearly uniform convexity, the drop property and...
The reciprocal Dunford–Pettis property of order in projective tensor products
We investigate whether the projective tensor product of two Banach spaces and has the reciprocal Dunford–Pettis property of order , , when and have the respective property.
The Schroeder-Bernstein index for Banach spaces
In relation to some Banach spaces recently constructed by W. T. Gowers and B. Maurey, we introduce the notion of Schroeder-Bernstein index SBi(X) for every Banach space X. This index is related to complemented subspaces of X which contain some complemented copy of X. Then we establish the existence of a Banach space E which is not isomorphic to Eⁿ for every n ∈ ℕ, n ≥ 2, but has a complemented subspace isomorphic to E². In particular, SBi(E) is uncountable. The construction of E follows the approach...
The Space of Differences of Convex Functions on [0, 1]
∗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]
The Steinitz constant of the plane.
The strong unicity constant and its applications
In this report we discuss the applications of the strong unicity constant and highlight its use in the minimal projection problem.
The strong unicity constant for projections.
The Szlenk index and the fixed point property under renorming.
The three space problem for smooth partitions of unity and C(K) spaces.
The topological complexity of sets of convex differentiable functions.
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
The unit ball of every infinite-dimensional normed linear space contains a (1+ɛ)-separated sequence