M-weak and L-weak compactness of b-weakly compact operators
We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).
Narrow operators (a survey)
Narrow operators are those operators defined on function spaces which are "small" at signs, i.e., at {-1,0,1}-valued functions. We summarize here some results and problems on them. One of the most interesting things is that if E has an unconditional basis then each operator on E is a sum of two narrow operators, while the sum of two narrow operators on L₁ is narrow. Recently this notion was generalized to vector lattices. This generalization explained the phenomena of sums: the set of all regular...
Narrow operators and rich subspaces of Banach spaces with the Daugavet property
Let X be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on X which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces X with the Daugavet property previously studied in the context of the classical spaces C(K) and L₁(μ).
Nature de l'image linéaire continue d'un espace de Banach dans un espace de Banach séparable
Near isometries of spaces of weak * continuous functions, with an application to Bochner spaces
Near smoothness of Banach spaces.
The aim of this paper is to discuss the concept of near smoothness in some Banach sequence spaces.
Nearly smooth points and near smoothness in Orlicz spaces
Nearly smooth points and near smoothness in Orlicz spaces are characterized. It is worth to notice that in the nonatomic case smooth points and nearly smooth points are the same, but in the sequence case they differ.
Necessary and sufficient condition for compactness of the embedding operator.
Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces
A necessary condition for Kostyuchenko type systems and system of powers to be a basis in (1 ≤ p < +∞) spaces is obtained. In particular, we find a necessary condition for a Kostyuchenko system to be a basis in (1 ≤ p < +∞).
New concepts in nondifferentiable programming
New examples of K-monotone weighted Banach couples
Some new examples of K-monotone couples of the type (X,X(w)), where X is a symmetric space on [0,1] and w is a weight on [0,1], are presented. Based on the property of w-decomposability of a symmetric space we show that, if a weight w changes sufficiently fast, all symmetric spaces X with non-trivial Boyd indices such that the Banach couple (X,X(w)) is K-monotone belong to the class of ultrasymmetric Orlicz spaces. If, in addition, the fundamental function of X is for some p ∈ [1,∞], then . At...
New examples of weakly compact approximation in Banach spaces.
New extension of the variational McShane integral of vector-valued functions
We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset of -dimensional Euclidean space . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from -dimensional closed non-degenerate intervals to open and bounded subsets of . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our...
New Gaussian Estimates for Enlarged Balls.
Non interpolation in Morrey-Campanato and block spaces
Nonaccessible filters in measure algebras and functionals on
(Non-)amenability of ℬ(E)
In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra ℬ(E) of all bounded linear operators on a Banach space E could ever be amenable if dim E = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros-Haydon result that solves the “scalar plus compact problem”: there is an infinite-dimensional Banach space E, the dual of which is ℓ¹, such that . Still, ℬ(ℓ²) is not amenable,...
Non-archimedean representations of compact groups
Non-Archimedean Umbral Calculus
Nonatomic Lipschitz spaces
We abstractly characterize Lipschitz spaces in terms of having a lattice-complete unit ball and a separating family of pure normal states. We then formulate a notion of "measurable metric space" and characterize the corresponding Lipschitz spaces in terms of having a lattice complete unit ball and a separating family of normal states.