PomeDefinition 22.1.14.CCAAC9DA4E2F Let $\omega $ be a closed real smooth positive $(1,1)$-form on $X$. We define the map
\[ P_{\theta +\omega }[\bullet ]_{\mathcal{I}}\colon \mathrm{PSH}^{\mathrm{NA}}(X,\theta )\rightarrow \mathrm{PSH}^{\mathrm{NA}}(X,\theta +\omega ) \]
as follows: Given $\Gamma \in \mathrm{PSH}^{\mathrm{NA}}(X,\theta )$, we define $P_{\theta +\omega }[\Gamma ]_{\mathcal{I}}$ as the element such that for any $\omega '\in \textup{Käh}(X)$, we have
\[ P_{\theta +\omega }[\Gamma ]_{\mathcal{I}}^{\theta +\omega +\omega '}=\Gamma ^{\theta +\omega +\omega '}. \]
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