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

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 Invertible Weighted Composition Operators on the Fock Space ofCN

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Liankuo Zhao
Keyword(s):  
Fock Space ◽  
Composition Operators ◽  
Complete Characterization ◽  
Weighted Composition Operators ◽  
Weighted Composition

We give a complete characterization of bounded invertible weighted composition operators on the Fock space ofCN.

Strict Topology on Spaces of Continuous Vector-Valued Functions

1979 ◽  
Vol 31 (4) ◽  
pp. 890-896 ◽  
Author(s):  
Seki A. Choo
Keyword(s):  
Tensor Product ◽  
Convex Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Locally Convex Space ◽  
Completely Regular ◽  
Vector Valued Functions ◽  
Bounded Continuous Functions ◽  
Vector Valued ◽  
Locally Convex

In this paper, X denotes a completely regular Hausdorff space, Cb(X) all real-valued bounded continuous functions on X, E a Hausforff locally convex space over reals R, Cb(X, E) all bounded continuous functions from X into E, Cb(X) ⴲ E the tensor product of Cb(X) and E. For locally convex spaces E and F, E ⴲ, F denotes the tensor product with the topology of uniform convergence on sets of the form S X T where S and T are equicontinuous subsets of E′, F′ the topological duals of E, F respectively ([11], p. 96). For a locally convex space G , G ′ will denote its topological dual.

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 Weighted composition operators on functional Hilbert spaces

1985 ◽  
Vol 31 (1) ◽  
pp. 117-126 ◽  
Author(s):  
R.K. Singh ◽  
R. David Chandra Kumar
Keyword(s):  
Hilbert Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Linear Operators ◽  
Weighted Composition Operators ◽  
Bounded Linear ◽  
Atomic Measure ◽  
Weighted Composition ◽  
Functional Hilbert Spaces

Let X be a non-empty set and let H(X) denote a Hibert space of complex-valued functions on X. Let T be a mapping from X to X and θ a mapping from X to C such that for all f in H(X), f ° T is in H(x) and the mappings CT taking f to f ° T and M taking f to θ.f are bounded linear operators on H(X). Then the operator CTMθ is called a weighted composition operator on H(X). This note is a report on the characterization of weighted composition operators on functional Hilbert spaces and the computation of the adjoint of such operators on L2 of an atomic measure space. Also the Fredholm criteria are discussed for such classes of operators.

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