【预告】学术报告（2024-29）12月11日——Spectrum of compression of the coordinate multiplier
Let $\mathcal{H}$ be a reproducing kernel Hilbert space of analytic functions over the unit disk $\mathbb{D}$. Let $T_z:~f\mapsto zf$ be the coordinate multiplier on $\mathcal{H}$. Suppose that $A$ is a zero set for $\mathcal{H}$ and $I_A$ is the invariant subspace for $T_z$ determined by $A$. Under some mild conditions, we prove that the spectrum of the compression of $T_z$ on $\mathcal{H}\ominus I_A$ is the closure of $A$. This covers the corresponding result in many classical function spaces. We give a uniform approach which does not rely on specific properties of a specific space.
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