Compact Differences of Composition Operators in Several Variables |
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Authors: | Katherine Heller Barbara D MacCluer Rachel J Weir |
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Institution: | 1.Department of Mathematics,University of Virginia,Charlottesville,USA;2.Department of Mathematics,Allegheny College,Meadville,USA |
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Abstract: | When φ and ψ are linear–fractional self-maps of the unit ball B
N
in
\mathbb CN,N 3 1{{\mathbb C}^N,N\geq 1}, we show that the difference Cj-Cy{C_{\varphi}-C_{\psi}} cannot be non-trivially compact on either the Hardy space H
2(B
N
) or any weighted Bergman space A2a(BN){A^2_{\alpha}(B_N)}. Our arguments emphasize geometrical properties of the inducing maps φ and ψ. |
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Keywords: | |
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