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Full-Text Articles in Analysis
Isolation And Component Structure In Spaces Of Composition Operators, Christopher Hammond, Barbara D. Maccluer
Isolation And Component Structure In Spaces Of Composition Operators, Christopher Hammond, Barbara D. Maccluer
Mathematics Faculty Publications
We establish a condition that guarantees isolation in the space of composition operators acting between H p (B N ) and H q (B N ), for 0 < p ≤ ∞, 0 < q < ∞, and N ≥ 1. This result will allow us, in certain cases where 0 < q < p ≤ ∞, completely to characterize the component structure of this space of operators.
The Norm Of A Composition Operator With Linear Symbol Acting On The Dirichlet Space, Christopher Hammond
The Norm Of A Composition Operator With Linear Symbol Acting On The Dirichlet Space, Christopher Hammond
Mathematics Faculty Publications
We obtain a representation for the norm of a composition operator on the Dirichlet space induced by a map of the form φ(z)=az+b. We compare this result to an upper bound for ‖Cφ‖ that is valid whenever φ is univalent. Our work relies heavily on an adjoint formula recently discovered by Gallardo-Gutiérrez and Montes-Rodríguez.