Topologies of some new sequence spaces, their duals, and the graphical representations of neighborhoods
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.
scientific article; zbMATH DE number 5935884
scientific article