Open AccessWEIGHTED COMPOSITION OPERATORS AND DYNAMICAL SYSTEMS
Author(s) -
Raj Singh,
Bhopinder Singh
Publication year - 1998
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.29.1998.4279
Subject(s) - mathematics , metrization theorem , hausdorff space , composition (language) , bounded function , space (punctuation) , regular polygon , dynamical systems theory , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , separable space , geometry , linguistics , philosophy , physics , quantum mechanics
Let $X$ be a completely regular Hausdorff space, $E$ a Hausdorff locally convex topological vector space, and $V$ a system of weights on $X$. Denote by $CV_b(X, E)$ ($CV_o(X, E)$) the weighted space of all continuous functions $f : X \to E$ such that $vf (X)$ is bounded in $E$ (respectively, $vf$ vanishes at infinity on $X$) for all $v \in V$. In this paper, we give an improved characterization of weighted composition operators on $CV_b(X, E)$ and present a linear dynamical system induced by composition operators on the metrizable weighted space $CV_o(\mathbb{R}, E)$.