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Some aspects of nuclear vector groups

Lydia Außenhofer (2001)

Studia Mathematica

In [2] W. Banaszczyk introduced nuclear groups, a Hausdorff variety of abelian topological groups which is generated by all nuclear vector groups (cf. 2.3) and which contains all nuclear vector spaces and all locally compact abelian groups. We prove in 5.6 that the Hausdorff variety generated by all nuclear vector spaces and all locally compact abelian groups (denoted by 𝒱₁) is strictly smaller than the Hausdorff variety of all nuclear groups (denoted by 𝒱₂). More precisely,...

Some aspects of the modern theory of Fréchet spaces.

Klaus D. Bierstedt, José Bonet (2003)

RACSAM

We survey some recent developments in the theory of Fréchet spaces and of their duals. Among other things, Section 4 contains new, direct proofs of properties of, and results on, Fréchet spaces with the density condition, and Section 5 gives an account of the modern theory of general Köthe echelon and co-echelon spaces. The final section is devoted to the developments in tensor products of Fréchet spaces since the negative solution of Grothendieck?s ?problème des topologies?.

Some characterization of locally nonconical convex sets

Witold Seredyński (2004)

Czechoslovak Mathematical Journal

A closed convex set Q in a local convex topological Hausdorff spaces X is called locally nonconical (LNC) if for every x , y ∈ Q there exists an open neighbourhood U of x such that ( U ∩ Q ) + 1 2 ( y - x ) ⊂ Q . A set Q is local cylindric (LC) if for x , y ∈ Q , x ≠ y , z ∈ ( x , y ) there exists an open neighbourhood U of z such that U ∩ Q (equivalently: b d ( Q ) ∩ U ) is a union of open segments parallel to [ x , y ] . In this paper we prove that these two notions are equivalent. The properties LNC and LC were investigated in [3], where the implication L N C ⇒ L C was proved in general, while...

Some characterizations of order weakly compact operator

Belmesnaoui Aqzzouz, Aziz Elbour (2011)

Mathematica Bohemica

We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.

Some characterizations of ultrabornological spaces

Manuel Valdivia (1974)

Annales de l'institut Fourier

Let U be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let F be an infinite-dimensional Banach space. Then F is the inductive limit of a family of spaces equal to E . The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let Ω be a non-empty open set in the euclidean n -dimensional space R n . Then F is the inductive limit of a family of spaces equal to D ( Ω ) .

Some common fixed point results for rational type contraction mappings in partially ordered metric spaces

Sumit Chandok (2013)

Mathematica Bohemica

The purpose of this paper is to establish some common fixed point results for f -nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977).

Currently displaying 81 – 100 of 310