Compact and quasinormal composition operators
Copyright policy )Compact and quasinormal composition operators
Let C ϕ {C_\phi } be a composition operator on L 2 ( λ ) {L^2}(\lambda ) , where λ \lambda is a σ \sigma -finite measure on a set X X . If X X is nonatomic, then Ridge proved that no one-to-one composition operator C ϕ {C_\phi } , with dense range is compact. This result is generalized in the paper by removing one-to-one and dense range conditions. The quasinormal composition operators are also characterized in terms of commutativity with the multiplication operator induced by the Radon-Nikodym derivative of the measure λ ϕ − 1 \lambda {\phi ^{ - 1}} with respect to λ \lambda .
Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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