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arXiv · 1006.2121

Compact differences of composition operators

Katherine Heller·Barbara D. MacCluer·Rachel J. Weir
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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 $C_φ-C_ψ$ cannot be non-trivially compact on either the Hardy space $H^2(B_N)$ or any weighted Bergman space $A^2_α(B_N)$. Our arguments emphasize geometrical properties of the inducing maps $φ$ and $ψ$.

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Katherine Heller, Barbara D. MacCluer, Rachel J. Weir. 2010-06-10. Compact differences of composition operators. https://arxiv.org/abs/1006.2121

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