Search results for "Fréchet space"

Variations of selective separability II: Discrete sets and the influence of convergence and maximality

2012

A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\in\omega)$ one can pick finite (respectively, one-point) subsets $F_n\subset D_n$ such that $\bigcup_{n\in\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \emph{d-separable} if it has a dense $\sigma$-discrete subspace. We call a space $X$ D-separable if for every sequence of …

Extension maps in ultradifferentiable and ultraholomorphic function spaces

2000

A characterization of Hajłasz–Sobolev and Triebel–Lizorkin spaces via grand Littlewood–Paley functions

2010

Abstract In this paper, we establish the equivalence between the Hajlasz–Sobolev spaces or classical Triebel–Lizorkin spaces and a class of grand Triebel–Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p ∈ ( n / ( n + 1 ) , ∞ ) , we give a new characterization of the Hajlasz–Sobolev spaces M ˙ 1 , p ( R n ) via a grand Littlewood–Paley function.

Fréchet Spaces of Holomorphic Functions without Copies of l 1

1996

Let X be a Banach space. Let Hw*(X*) the Frechet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of Hw*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l1 when this space contains no copy of l1. We also show that if X is an Asplund space, then Hw*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund.

Third-order iterative methods without using any Fréchet derivative

2003

AbstractA modification of classical third-order methods is proposed. The main advantage of these methods is they do not need to evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming the second divided difference is bounded and a punctual condition, is analyzed. Finally, some numerical results are presented.

Basic Sequences in the Dual of a Fréchet Space

2001

A note on best approximation in 0-complete partial metric spaces

2014

We study the existence and uniqueness of best proximity points in the setting of 0-complete partial metric spaces. We get our results by showing that the generalizations, which we have to consider, are obtained from the corresponding results in metric spaces. We introduce some new concepts and consider significant theorems to support this fact.

Banach spaces which are somewhat uniformly noncreasy

2003

AbstractWe consider a family of spaces wider than r-UNC spaces and we give some fixed point results in the setting of these spaces.

Holomorphic Mappings of Bounded Type on (DF)-Spaces

1992

We study the holomorphic functions of bounded type defined on (DF)-spaces. We prove that they are of uniformly bounded type. The space of all these functions is a Frechet space with its natural topology. Some consequences and related results are obtained.

A note on Taskinen's counterexamples on the problem of topologies of Grothendieck

1989

By the work of Taskinen (see [4, 5]), we know that there is a Fréchet space E such that Lb(E, l2) is not a (DF)-space. Moreover there is a Fréchet–Montel space F such that is not (DF). In this second example, the duality theorem of Buchwalter (cf. [2, §45.3]) can be applied to obtain that and hence is a (gDF)-space (cf. [1, Ch. 12 or 3, Ch. 8]). The (gDF)-spaces were introduced by several authors to extend the (DF)-spaces of Grothendieck and to provide an adequate frame to consider strict topologies.