On the Leontief's problem in Banach lattices
On the Lifshits Constant for Hyperspaces
The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
On the local moduli of squareness
We introduce the notions of pointwise modulus of squareness and local modulus of squareness of a normed space X. This answers a question of C. Benítez, K. Przesławski and D. Yost about the definition of a sensible localization of the modulus of squareness. Geometrical properties of the norm of X (Fréchet smoothness, Gâteaux smoothness, local uniform convexity or strict convexity) are characterized in terms of the behaviour of these moduli.
On the locally uniformly weak star rotundity of Orlicz spaces.
In the paper, a sufficient and necessary condition is given for the locally uniformly weak star rotundity of Orlicz spaces with Orlicz norms.
On the LURWC property of Orlicz sequence space.
Necessary and sufficient conditions for URWC points and LURWC property are given in Orlicz sequence space lM.
On the moduli of convexity and smoothness
On the modulus of measures with values in topological Riesz spaces.
The paper is devoted to a study of some aspects of the theory of (topological) Riesz space valued measures. The main topics considered are the following. First, the problem of existence (and, particularly, the so-called proper existence) of the modulus of an order bounded measure, and its relation to a similar problem for the induced integral operator. Second, the question of how properties of such a measure like countable additivity, exhaustivity or so-called absolute exhaustivity, or the properties...
On the modulus of one-parameter semigroups.
On the modulus of -convexity.
On the modulus of -convexity of Ji Gao.
On the M-structure of the operator space L(CK)
On the non- and locally uniformly non- properties, and copies in Musielak-Orlicz spaces
On the non-equivalence of rearranged Walsh and trigonometric systems in
We consider the question of whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in for some p ≠ 2. We show that this question is closely related to a combinatorial problem. This enables us to prove non-equivalence for a number of rearrangements. Previously this was known for the Walsh-Paley order only.
On the nonexistence of bilipschitz parametrizations and geometric problems about A∞-weights.
How can one recognize when a metric space is bilipschitz equivalent to an Euclidean space? One should not take the abstraction of metric spaces too seriously here; subsets of Rn are already quite interesting. It is easy to generate geometric conditions which are necessary for bilipschitz equivalence, but it is not clear that such conditions should ever be sufficient. The main point of this paper is that the optimistic conjectures about the existence of bilipschitz parametrizations are wrong. In...
On the norm of a projection onto the space of compact operators
Let X and Y be Banach spaces and let 𝓐(X,Y) be a closed subspace of 𝓛(X,Y), the Banach space of bounded linear operators from X to Y, containing the subspace 𝒦(X,Y) of compact operators. We prove that if Y has the metric compact approximation property and a certain geometric property M*(a,B,c), where a,c ≥ 0 and B is a compact set of scalars (Kalton's property (M*) = M*(1, {-1}, 1)), and if 𝓐(X,Y) ≠ 𝒦(X,Y), then there is no projection from 𝓐(X,Y) onto 𝒦(X,Y) with norm less than max|B| + c....
On the number of non-isomorphic subspaces of a Banach space
We study the number of non-isomorphic subspaces of a given Banach space. Our main result is the following. Let be a Banach space with an unconditional basis ; then either there exists a perfect set P of infinite subsets of ℕ such that for any two distinct A,B ∈ P, , or for a residual set of infinite subsets A of ℕ, is isomorphic to , and in that case, is isomorphic to its square, to its hyperplanes, uniformly isomorphic to for any D ⊂ ℕ, and isomorphic to a denumerable Schauder decomposition...
On the Numerical Range in Reflexive Banach Spaces.
On the o-Spektrum of Regular Operators and the Spectrum of Measures.
On the p-drop theorem, 1 ≤ p ≤∞.
On the points of multivaluedness of metric projections in separable Banach spaces