LaTeX complains Limit controls must follow a math operator. \textbf{G} := \parallel\limits about the following snippet.
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\textbf{G} := \parallel\limits_{\pi \in \mathcal{P}} \textbf{G}^{\pi}
\end{equation}
\end{document}
What is a possible workaround to apply \limits to \parallel?
Maybe you want a symbol similar to \sum:
\documentclass{article}
\usepackage{mathtools,graphicx}
\makeatletter
\newcommand{\parop}{\DOTSB\parop@\slimits@}
\newcommand{\parop@}{\mathop{\vphantom{\sum}\mathpalette\delimiter@to@op\Vert}}
\newcommand{\delimiter@to@op}[2]{%
\begingroup
\sbox\z@{$#1\sum$}%
\vcenter{\hbox{\resizebox{!}{\ht\z@}{$\m@th#2$}}}%
\endgroup
}
\makeatother
\begin{document}
\begin{equation}
\textbf{G} \coloneqq \parop_{\pi \in \mathcal{P}} \textbf{G}^{\pi}
\end{equation}
\begin{equation}
\sum_{\pi \in \mathcal{P}} \parop_{\pi \in \mathcal{P}}
\end{equation}
\begin{equation}
\textstyle \sum_{\pi \in \mathcal{P}} \parop_{\pi \in \mathcal{P}}
\scriptstyle \sum_{\pi \in \mathcal{P}} \parop_{\pi \in \mathcal{P}}
\scriptscriptstyle \sum_{\pi \in \mathcal{P}} \parop_{\pi \in \mathcal{P}}
\end{equation}
\end{document}
For a quick and dirty one-time-use solution, make it a math operator.
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\textbf{G} := \mathop{\parallel}\limits_{\pi \in \mathcal{P}} \textbf{G}^{\pi}
\end{equation}
\end{document}
