TY - JOUR
T1 - Weighted composition operators on nonlocally convex weighted spaces of continuous functions
AU - Manhas, J. S.
AU - Singh, R. K.
PY - 1998
Y1 - 1998
N2 - Let V be a system of weights on a completely regular Hausdorff space X and let B(E) be the topological vector space of all continuous linear operators on a general topological vector space E. Let CV0(X, E) and CVb(X, E) be the weighted spaces of vector-valued continuous functions (vanishing at infinity or bounded, respectively) which are not necessarily locally convex. In the present paper, we characterize in this general setting the weighted composition operators Wπ, Φ on CV0(X, E) (or CVb(X, E)) induced by the operator-valued mappings π : X → B(E) (or the vector-valued mappings π : X → E, where E is a topological algebra) and the self-map Φ of X. Also, we characterize the mappings π : X → B(E) (or π : x → E) and π : X → X which induce the compact weighted composition operators on these weighted spaces of continuous functions.
AB - Let V be a system of weights on a completely regular Hausdorff space X and let B(E) be the topological vector space of all continuous linear operators on a general topological vector space E. Let CV0(X, E) and CVb(X, E) be the weighted spaces of vector-valued continuous functions (vanishing at infinity or bounded, respectively) which are not necessarily locally convex. In the present paper, we characterize in this general setting the weighted composition operators Wπ, Φ on CV0(X, E) (or CVb(X, E)) induced by the operator-valued mappings π : X → B(E) (or the vector-valued mappings π : X → E, where E is a topological algebra) and the self-map Φ of X. Also, we characterize the mappings π : X → B(E) (or π : x → E) and π : X → X which induce the compact weighted composition operators on these weighted spaces of continuous functions.
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U2 - 10.1007/bf02771088
DO - 10.1007/bf02771088
M3 - Article
AN - SCOPUS:27844467304
SN - 0133-3852
VL - 24
SP - 275
EP - 292
JO - Analysis Mathematica
JF - Analysis Mathematica
IS - 1
ER -