Compact and weakly compact weighted composition operators on weighted spaces of continuous functions

1997 ◽  
Vol 29 (1) ◽  
pp. 63-69 ◽  
Author(s):  
J. S. Manhas ◽  
R. K. Singh
Keyword(s):  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Weighted Composition Operators ◽  
Weakly Compact ◽  
Spaces Of Continuous Functions ◽  
Weighted Composition

Hypercyclic, mixing, and chaotic C0-semigroups induced by semiflows

2007 ◽  
Vol 27 (5) ◽  
pp. 1599-1631 ◽  
Author(s):  
T. KALMES
Keyword(s):  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Composition Operators ◽  
Integrable Functions ◽  
Spaces Of Continuous Functions ◽  
Weighted Composition ◽  
Topologically Mixing

AbstractWe characterize when C0-semigroups induced by semiflows are hypercyclic, topologically mixing, or chaotic both on spaces of integrable functions and on spaces of continuous functions. Furthermore, we give characterizations of transitivity for weighted composition operators on these spaces.

scholarly journals On characterizations of weighted composition opeartors on non-locally convex weighted spaces of continuous functions

2000 ◽  
Vol 31 (1) ◽  
pp. 1-8 ◽  
Author(s):  
S. D. Sharma ◽  
Kamaljeet Kour ◽  
Bhopinder Singh
Keyword(s):  
Hausdorff Space ◽  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Completely Regular ◽  
Hausdorff Topological Vector Space ◽  
Spaces Of Continuous Functions ◽  
Weighted Composition ◽  
Locally Convex ◽  
Convex Setting

For a system $V$ of weights on a completely regular Hausdorff space $X$ and a Hausdorff topological vector space $E$, let $ CV_b(X,E)$ and $ CV_0(X,E)$ respectively denote the weighted spaces of continuouse $E$-valued functions $f$ on $X$ for which $ (vf)(X)$ is bounded in $E$ and $vf$ vanishes at infinity on $X$ all $ v\in V$. On $CV_b(X,E)(CV_0(X,E))$, consider the weighted topology, which is Hausdorff, linear and has a base of neighbourhoods of 0 consising of all sets of the form: $ N(v,G)=\{f:(vf)(X)\subseteq G\}$, where $v\in V$ and $G$ is a neighbourhood of 0 in $E$. In this paper, we characterize weighted composition operators on weighted spaces for the case when $V$ consists of those weights which are bounded and vanishing at infinity on $X$. These results, in turn, improve and extend some of the recent works of Singh and Singh [10, 12] and Manhas [6] to a non-locally convex setting as well as that of Singh and Manhas [14] and Khan and Thaheem [4] to a larger class of operators.

scholarly journals WEIGHTED COMPOSITION OPERATORS AND DYNAMICAL SYSTEMS

1998 ◽  
Vol 29 (2) ◽  
pp. 101-107
Author(s):  
R. K. SINGH ◽  
BHOPINDER SINGH
Keyword(s):  
Hausdorff Space ◽  
Weighted Space ◽  
Composition Operators ◽  
Continuous Functions ◽  
Weighted Composition Operators ◽  
Linear Dynamical System ◽  
Completely Regular ◽  
Weighted Composition ◽  
Locally Convex

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 $CV_o(\mathbb{R}, E)$.

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