相关论文: A note on convex renorming and fragmentability

We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with $G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise those Banach spaces which admit…

The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with $C^k$ smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of $B_{X^*}$, namely…

We prove in this article that every Borelian measure, for example, the distribution of a random variable, in separable Banach space has a support which is compact embedded Banach subspace; and prove that if the norm of the random variable…

We study dentable maps from a closed convex subset of a Banach space into a metric space as an attempt of generalize the Radon-Nikod\'ym property to a "less linear" frame. We note that a certain part of the theory can be developed in rather…

In this paper, we completely settle several of the open questions regarding the relationships between the three most fundamental forms of set convergence. In particular, it is shown that Wijsman and slice convergence coincide precisely when…

In this paper we show that if $(y_n)$ is a seminormalized sequence in a Banach space which does not have any weakly convergent subsequence, then it contains a wide-$(s)$ subsequence $(x_n)$ which admits an equivalent convex basic sequence.…

Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…

We show that for any given norm ball or proper cone, weak membership in its dual ball or dual cone is polynomial-time reducible to weak membership in the given ball or cone. A consequence is that the weak membership or membership problem…

The abscissas of convergence, uniform convergence and absolute convergence of vector valued Dirichlet series with respect to the original topology and with respect to the weak topology $\sigma(X,X')$ of a locally convex space $X$, in…

In order to measure qualitative properties we introduce a notion of a type for arbitrary normed spaces which measures the worst possible growth of partial sums of sequences weakly converging to zero. The ideas can be traced back to Banach…

Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…

We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with…

We give a new proof of the "weakly admissible implies admissible" theorem of Colmez and Fontaine describing the semi-stable p-adic representations. We study Banach-Colmez spaces, i.e. p-adic Banach spaces with the extra data of a…

In this paper, we embed metric space endowed with a convex combination operation, named convex combination space, into a Banach space and the embedding preserves the structures of metric and convex combination. For random element taking…

We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their $\omega$-iterates. We introduce the notions of convexifiable and sublinear measure of non-compactness and…

We present some extensions of classical results that involve elements of the dual of Banach spaces, such as Bishop-Phelp's theorem and James' compactness theorem, but restricting to sets of functionals determined by geometrical properties.…

Concentration compactness method is a powerful techniques for establishing existence of minimizers for inequalities and of critical points of functionals in general. The paper gives a functional-analytic formulation for the method in Banach…

We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested against all the metric functionals defined on said space. When…

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…

In terms of fragmentability, we describe a new class of Banach spaces which do not contain weak-G_delta open bounded subsets. In particular, none of these spaces is isomorphic to a separable polyhedral space.