Compact differences of composition operators

Details Compact differences of composition operators Compact differences of composition operators

2010-06-10

arxiv.org/abs/1006.2121v1

Mathematics

Functional Analysis

20 pages

Scientific paper

When $\varphi$ and $\psi$ 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 $\varphi$ and $\psi$.

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