Abstract
When φ and ψ are linear–fractional self-maps of the unit ball B N in \({{\mathbb C}^N,N\geq 1}\), we show that the difference \({C_{\varphi}-C_{\psi}}\) cannot be non-trivially compact on either the Hardy space H 2(B N ) or any weighted Bergman space \({A^2_{\alpha}(B_N)}\). Our arguments emphasize geometrical properties of the inducing maps φ and ψ.
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R. J. Weir would like to thank the Allegheny College Academic Support Committee for funding provided during the development of this paper.
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Heller, K., MacCluer, B.D. & Weir, R.J. Compact Differences of Composition Operators in Several Variables. Integr. Equ. Oper. Theory 69, 247–268 (2011). https://doi.org/10.1007/s00020-010-1840-5
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DOI: https://doi.org/10.1007/s00020-010-1840-5