Compact differences of composition operators

Abstract

When $\phi$ and $\psi$ are linear-fractional self-maps of the unit ball $B_N$ in ${\mathbb{C}}^N$, $N\ge 1$, we show that the difference $C_{\phi }-C_{\psi }$ cannot be non-trivially compact on either the Hardy space $H^2(B_N)$ or any weighted Bergman space $A_{\alpha }^2(B_N)$. Our arguments emphasize geometrical properties of the inducing maps $\phi$ and $\psi$.

20 pages

References in corpus (1)

• Toeplitz-Composition C*-Algebras