The Grothendieck property for injective tensor products of Banach spaces
The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces
We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically normal spaces....
The Hahn sequence space. III.
The Hahn-Banach Theorem surveyed [Book]
The Hahn-Banach-Kantorovich formula for a lattice subdifferential.
The heredity problem for weakly compactly generated Banach spaces
The Hyers-Ulam-Aoki Type Stability of Some Functional Equations on Banach Lattices
In Agbeko (2012) the Hyers-Ulam-Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.
The hypo-Euclidean norm of an -tuple of vectors in inner product spaces and applications.
The ideal property of tensor products of Banach lattices with applications to the local structure of spaces of absolutely summing operators
The impact of the Radon-Nikodym property on the weak bounded approximation property.
A Banach space X is said to have the weak λ-bounded approximation property if for every separable reflexive Banach space Y and for every compact operator T : X → Y, there exists a net (Sα) of finite-rank operators on X such that supα ||TSα|| ≤ λ||T|| and Sα → IX uniformly on compact subsets of X.We prove the following theorem. Let X** or Y* have the Radon-Nikodym property; if X has the weak λ-bounded approximation property, then for every bounded linear operator T: X → Y, there exists a net (Sα)...
The inclusion theorem for multiple summing operators
We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.
The instability of nonseparable complete Erdős spaces and representations in ℝ-trees
One way to generalize complete Erdős space is to consider uncountable products of zero-dimensional -subsets of the real line, intersected with an appropriate Banach space. The resulting (nonseparable) complete Erdős spaces can be fully classified by only two cardinal invariants, as done in an earlier paper of the authors together with J. van Mill. As we think this is the correct way to generalize the concept of complete Erdős space to a nonseparable setting, natural questions arise about analogies...
The isomorphic problem of envelopes
The James constant of normalized norms on .
The JNR Property and the Borel Structure of a Banach Space
Research partially supported by a grant of Caja de Ahorros del Mediterraneo.In this paper we study the property of having a countable cover by sets of small local diameter (SLD for short). We show that in the context of Banach spaces (JNR property) it implies that the Banach space is Cech-analytic. We also prove that to have the JNR property, to be σ- fragmentable and to have the same Borel sets for the weak and the norm topologies, they all are topological invariants of the weak topology. Finally, by...
The Johnson-Lindenstrauss space.
The Joly's construction: A common property of some generalized orthogonalities.
The Kadec-Pełczyński-Rosenthal subsequence splitting lemma for JBW*-triple preduals
Any bounded sequence in an L¹-space admits a subsequence which can be written as the sum of a sequence of pairwise disjoint elements and a sequence which forms a uniformly integrable or equiintegrable (equivalently, a relatively weakly compact) set. This is known as the Kadec-Pełczyński-Rosenthal subsequence splitting lemma and has been generalized to preduals of von Neuman algebras and of JBW*-algebras. In this note we generalize it to JBW*-triple preduals.
The Krein-Šmulian theorem and its extension
The Kreps-Yan theorem for Banach ideal spaces.