On projections and unconditional bases in direct sums of Banach spaces
On projections and unconditional bases in direct sums of Banach spaces II
On projections in Banach space
On projections in H¹ and BMO
On projections in spaces of bounded analytic functions with applications
On projections on subspaces of codimension one
On Property β of Rolewicz in Köthe-Bochner Function Spaces
It is proved that the Köthe-Bochner function space E(X) has property β if and only if X is uniformly convex and E has property β. In particular, property β does not lift from X to E(X) in contrast to the case of Köthe-Bochner sequence spaces.
On property (β) of Rolewicz in Köthe-Bochner sequence spaces
We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend and improve...
On property (β) of Rolewicz in Musielak-Orlicz sequence spaces equipped with the Orlicz norm
We prove that the Musielak-Orlicz sequence space with the Orlicz norm has property (β) iff it is reflexive. It is a generalization and essential extension of the respective results from [3] and [5]. Moreover, taking an arbitrary Musielak-Orlicz function instead of an N-function we develop new methods and techniques of proof and we consider a wider class of spaces than in [3] and [5].
On quotients of which are quotients of
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 reiteration and the behaviour of weak compactness under certain interpolation methods.
This article deals with K- and J-spaces defined by means of polygons. First we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We also show optimality of the weak compactness results.
On relatively disjoint families of measures, with some applications to Banach space theory
On Representations in Banach Spaces.
On Residuality of the Set of Rotund Norms on a Banach Space.
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 restriction properties of multiplication operators.
On Reuleaux triangles in Minkowski planes.