Compact differences of composition operators
msra(2010)
摘要
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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关键词
unit ball,hardy space,composition operator,functional analysis
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