Topologies of some new sequence spaces, their duals, and the graphical representations of neighborhoods
type: Item
instance of: scholarly article
title: Topologies of some new sequence spaces, their duals, and the graphical representations of neighborhoods
zbMATH Open document ID: 1228.54029
author: Eberhard Malkowsky
author: Vesna Velickovic
published in: Topology and its Applications
publication date: 2011-08-04T00:00:00Z
review text: Let \(\omega\) denote the linear topological space consisting of sequences of complex numbers \(x= (x_k)^\infty_{k=1}\) endowed with the metric \[ d(x,y)= \sum^\infty_{k=1} {1\over 2^k} {|x_k- y_k|\over 1+|x_k- y_k|} \] for \(x,y\in\omega\). By an FK space is understood a Fréchet subspace of \(\omega\). It is characterized by the property that every Fréchet space with a Schauder basis is congruent to an FK space. The authors study these spaces and their duals claiming that they have an important application in crystallography, in particular in the growth of cyrstals.
reviewed by: Ludvík Janoš
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 40H05
zbMATH DE Number: 5935884
zbMATH Keywords: topologies and neighborhoods
zbMATH Keywords: \(FK\) spaces
zbMATH Keywords: dual spaces
zbMATH Keywords: visualization
zbMATH Keywords: computer graphics
MaRDI profile type: Publication
full work available at URL: j.topol.2011.05.011
OpenAlex ID: W1992791342
cites work: Q4338536
cites work: Q4291799
cites work: Q5509268
cites work: Q3312652
cites work: Q5539950
cites work: Q5573691
cites work: The Sequence Spaces l (pv ) and m (pv )
cites work: The Structure of the Sequence Spaces of Maddox
cites work: A study of certain sequence spaces of Maddox and a generalization of a theorem of Iyer
cites work: Q5558676
cites work: Q5588841
cites work: Q4870698
DOI: 10.1016/J.TOPOL.2011.05.011
Recommended article: Topological properties of the sequence spaces \(S^{\nu }\)
Recommended article: Some topologic and geometric properties of new Catalan sequence spaces
Recommended article: Topological duals of some paranormed sequence spaces
Recommended article: Some topological and geometrical properties of a new difference sequence space
Recommended article: Some topological and geometrical properties of new Banach sequence spaces
Recommended article: Topologization of entire sequences spaces
Recommended article: Duality of new sequence spaces
Recommended article: The \(\sigma\)-duals of sequence spaces
Recommended article: On the \(f\)-dual of sequence spaces
Recommended article: Q3191342
description: scientific article; zbMATH DE number 5935884