Example 20.2.16`50B7DFD48C9D`

Example 20.2.16.50B7DFD48C9D Let $\varphi \in \mathrm{QPSH}(X)$. Take a closed real smooth $(1,1)$-form $\theta $ on $X$ such that $\varphi \in \mathrm{PSH}(X,\theta )_{>0}$, then

\[ \operatorname{Tr}_ X(\varphi )\sim _ P P_{\theta }[\varphi ]_{\mathcal{I}},\quad \operatorname{Tr}^{\theta }_ X(\varphi ) = P_{\theta }[\varphi ]_{\mathcal{I}}. \]

In particular, the trace operator can be regarded as a generalization of the $\mathcal{I}$-envelope.

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@misc{pome-tag-50B7DFD48C9D,
  author = {{Pome contributors}},
  title = {Example 20.2.16},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/50B7DFD48C9D/}
}

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Example 20.2.1650B7DFD48C9D

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Example 20.2.16`50B7DFD48C9D`