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Isolation and Component Structure in Spaces of Composition Operators

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Abstract.

We establish a condition that guarantees isolation in the space of composition operators acting between Hp(B N ) and Hq(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.

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  1. Christopher Hammond

    Present address: Department of Mathematics and Computer Science, Connecticut College, Box 5384, 270 Mohegan Avenue, New London, CT, 06320-4196, USA

Authors and Affiliations

  1. Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA, 22904-4137, USA

    Christopher Hammond & Barbara D. MacCluer

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  1. Christopher Hammond
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  2. Barbara D. MacCluer
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Correspondence to Christopher Hammond.

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Hammond, C., MacCluer, B.D. Isolation and Component Structure in Spaces of Composition Operators. Integr. equ. oper. theory 53, 269–285 (2005). https://doi.org/10.1007/s00020-004-1308-6

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  • DOI: https://doi.org/10.1007/s00020-004-1308-6

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