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Let $${(e_n)_{n=1}^\infty}$$ be the unit basis of the Banach space c0. In this paper we prove that, if X is a separable Banach space, there is a closed bounded absolutely convex subset B of c0 which has the following properties: (1) $${e_j\in B, j=1,2,\ldots'}$$ , and $${(e_n)_{n=1}^\infty}$$ is a monotone shrinking basis of (c0)B. (2) (c0)B has a topological complement Z in...
Every finite group G may act as an automorphism group of Klein surfaces either bordered or unbordered either orientable or non-orientable. For each group the minimum genus receives different names according to the topological features of the surface X on which it acts. If X is a bordered surface the genus is called the real genus ρ(G). If X is a non-orientable unbordered surface the genus is called...
We use renormings and generic differentiability of convex functions to prove some results on farthest points in sets in Banach spaces. As a corollary, we obtain an alternative proof of the Lindenstrauss–Troyanski result on representation of weakly compact convex sets by means of strongly exposed points. We use this approach to simplify former proofs of several known results in this area.
In a paper written some 25 years ago, I distinguished three contexts in which one might wish to combine expert judgements of uncertainty: the expert problem, the group decision problem and the textbook problem. Over the intervening years much has been written on the first two, which have the focus of a single decision context, but little on the third, though the closely related field of meta-analysis...
We prove that if M is either a compact g.o. space which is not naturally reductive, or a g.o. space which admits a transitive non-compact semisimple Lie group of isometries and is not naturally reductive, then its Jacobi osculating rank is not always constant.
In this paper we introduce the densifiable sets, a new class of subsets of metric spaces which are between the Peano continua and the class of precompact and connected sets. In $${\mathbb{R}^{n}}$$ , for the subsets of non-void interior, the class of densifiable sets has been characterized.
We study some topological properties of trees with the interval topology. In particular, we characterize trees which admit a 2-fibered compactification and we present two examples of trees whose one-point compactifications are Rosenthal compact with certain renorming properties of their spaces of continuous functions.
In this note we introduce the notion of smooth module to extend results from homology theory of Banach algebras to the locally convex category. A complete locally convex module over an m-convex algebra is shown to be smooth if and only if it is topologically isomorphic to a reduced inverse limit of Banach modules over Banach algebras. Stability properties for smoothness are discussed and conditions...
Dirichlet (J Reine Angew Math 24, 1842) announced a generalization of his class number formula for real quadratic fields to biquadratic fields containing $${\mathbb{Q}(i)}$$ , by replacing the circular trigonometric functions with certain elliptic trigonometric functions. Subsequently, Nazimow (Ann Sci École Norm Sup (3) 5:147–176, 1888) published the corresponding formula. Here we analyze the...
We get some necessary and sufficient conditions for the very weak solvability of the beam equation stated in terms of powers of the distance to the boundary, accordingly to the boundary condition under consideration. We get a L1-estimate by using an abstract result due to Crandall and Tartar. Applications to some nonlinear perturbed equations and to the eventual positivity of the solution of the...
Countable projective limits of countable inductive limits, so-called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen et al., who analyzed locally convex properties in terms of the defining double sequence of weights. We complement their results by considering a defining sequence which is the product of two single sequences. By associating these...
In this paper, we derive a new formula for the subdifferential of the supremum of an arbitrary family of extended real-valued functions, in terms of the approximate subgradients of well chosen convex combinations of the data functions. The data functions are neither convex nor lower semicontinuous, but in this paper we assume that the supremum of the second conjugates of the data functions is proper...
We consider a semistability property for a solution of variational inclusion of the form $${0\in\varphi(z)+F(z)}$$ where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map. We show that this property ensures interesting results for the order of convergence for a Hummel-Seebeck type method.
We present here what, as far as we know, is a real novelty: a computer package that can automatically generate railway maps of a certain network at any (past) date requested, using different colors to show the type of line. The input is: (1) a set of historical events, (2) the graph of the railway network at its maximum extension and (3) a list of geographical coordinates of stations, junctions, loading...
This survey paper collects some of older and quite new concepts and results from descriptive set topology applied to study certain infinite-dimensional topological vector spaces appearing in Functional Analysis, including Fréchet spaces, (LF)-spaces, and their duals, (DF)-spaces and spaces of continuous real-valued functions C(X) on a completely regular Hausdorff space X. Especially (LF)-spaces and...
In this paper we prove that if Y is a reflexive subspace of a Banach space X, then L∞(μ, Y) is simultaneously proximinal in L∞(μ, X). Furthermore if X is reflexive and μ0 is the restriction of μ to a sub-σ-algebra, then L∞(μ0, X) is simultaneously proximinal in L∞(μ, X).
Let $${\phi}$$ be an analytic self-map of the open unit disk $${\mathbb{D}}$$ in the complex plane. This map induces a composition operator followed by differentiation $${DC_{\phi}}$$ acting between weighted Banach spaces of holomorphic functions. We give a characterization for such an operator to be bounded resp. compact in terms of the involved weights as well as the function ...
The big computer algebra systems like Maple are no longer restricted to symbolic computations, but are becoming general purpose tools for engineers, mathematicians, and scientists instead. We have worked for a long time with many-valued logics and we believe that a flexible and comfortable tool that allowed to perform logical computations (for instance, to explore properties) in any existing or proposed...
We prove the existence of coincidence points and common fixed points for multivalued f-weak contraction mappings which assume closed values only. As an application, related common fixed point, invariant approximation, random coincidence point and random invariant approximation results are also obtained. Our results provide extensions as well as substantial improvements of several well known results...
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