On convexity and smoothness of Banach space
On exposed semigroup homomorphisms.
On extremal structure of weakly locally compact convex sets in Banach spaces
On finite dimensional subspaces of Banach spaces with local unconditional structure
On flatness and some ergodic properties of Banach spaces
On Inductive Limits of Banach Spaces.
On Kadec-Klee norms on Banach spaces
On locally uniformly convex and differentiable norms in certain non-separable Banach spaces
On minimal sequences of type and bounded biorthogonal systems in Banach spaces
On one generalization of weakly compactly generated Banach spaces
On perfectly homogeneous bases in quasi-Banach spaces.
On prequojections and their duals.
The paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in the structure theory of Fréchet spaces. The structure of prequojections was studied by G. Metafune and V. B. Moscatelli, who also gave a survey of the subject. Answering a question of these authors we show that their result on duals of prequojections cannot be generalized from the separable case to the case of spaces of arbitrary cardinality. We also introduce a special class...
On -reflexive Banach spaces
A Banach space is called -reflexive if for any cover of by weakly open sets there is a finite subfamily covering some ball of radius 1 centered at a point with . We prove that an infinite-dimensional separable Banach space is -reflexive (-reflexive for some ) if and only if each -net for has an accumulation point (resp., contains a non-trivial convergent sequence) in the weak topology of . We show that the quasireflexive James space is -reflexive for no . We do not know...
On reflexivity and summability
On regularization in superreflexive Banach spaces by infimal convolution formulas
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex functions converging to f uniformly on bounded sets and...
On relatively disjoint families of measures, with some applications to Banach space theory
On Representations in Banach Spaces.
On restricted weak upper semicontinuous set valued mappings and reflexivity
È noto che se uno spazio di Banach è quasi-smooth (cioè, la sua applicazione di dualità è debolmente semicontinua superiormente in senso ristretto), allora il suo duale non ha sottospazi chiusi normanti propri. Inoltre, se uno spazio di Banach ha una norma equivalente la cui applicazione di dualità ha un grafo che contiene superiormente un'applicazione debolmente semicontinua superiormente in senso ristretto, allora lo spazio è Asplund. Dimostriamo che se uno spazio di Banach ha una norma equivalente...
On self-conjugate Banach spaces
On shrinking basic sequences in Banach spaces