\hyperref delimiters, brackets, norms, parenthesis using \left and \right (suspending hyperref)

Question

I would like the norm-symbol \left\| \right\|_p to be linked to its definition, but I don't want its interior (x for example) to be linked. (And of course I want them to adjust their size automatically - that's why I use \left and \right)

Something like \hyperref[def:norm1]{\left\| {\suspendHyperref #1} \continueHyperref \right\|_1 } would be great! (firefox' build in pdf-reader hilights links on mouseover - so it would be awesome if the right side of the norm symbol \right_p also highlights, when I move the mouse over the left side of the norm symbol \left\| in firefox, but this is not my number 1 priority)

At least something like \hyperref[def:norm2]{\left\| } #1 \hyperref[def:norm2]{\right\|_2 } would be quite good, but this doesn't work because \left and \right form a group (like described in this post)

The following MWE produces a result that looks like I want it to look, but doesn't link correctly. Especially in eq. (1) the inner l_2-norm in the nested norms isn't linked correctly (because everything inside the outer l_1-norm is linked to the l_1-norm).

\documentclass[a4paper,11pt]{report}
\usepackage[colorlinks=true]{hyperref}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{definition}[theorem]{Definition}

\newcommand{\normOne}[1]{\hyperref[def:norm1]{\left\| {\normalcolor #1} \right\|_1 }}
\newcommand{\normTwo}[1]{\hyperref[def:norm2]{\left\| {\normalcolor #1} \right\|_2 }}

\begin{document}

\begin{definition}[$\ell_1-Norm$]\label{def:norm1}
\[ \normOne{x} := \sum_{i=1}^{n} \left| x_i \right|  \]
\end{definition}
\begin{definition}[$\ell_2-Norm$]\label{def:norm2}
\[ \normTwo{x} := \left( \sum_{i=1}^{n} \left| x_i \right|^2 \right)^{\frac{1}{2}} \]
\end{definition}

many pages later...

\begin{equation}
\normOne{ \left( \normTwo{y} - 3 \right) \hat{A}x}
\end{equation}

\end{document}

Maybe the idea of one of the answers to this question can be adopted to my problem, but unfortunately I don't understand all of these solutions well enough to know how to adopt them properly.

Answer 1

The essential part of my solution:

\newcommand{\BracKern}{\kern-\nulldelimiterspace}%https://tex.stackexchange.com/a/54035/128042

\newcommand{\linkedBrac}[5][]{% #2,#4 = left/right bracket type; #5 = label of link-target; optional argument #1: one can insert something like \color{green} here 
        \mathopen{\hyperref[#5]{#1\left#2\vphantom{#3}\BracKern\right.}}% left bracket
        #3%  content
        \mathclose{\hyperref[#5]{#1\left.\BracKern\vphantom{#3}\right#4}}% right bracket
}

\newcommand{\normTwo}[1]{\linkedBrac{\|}{#1}{\|_2}{def:norm2}}
\newcommand{\floor}[1]{\linkedBrac[\color{green}]{\lfloor}{#1}{\rfloor}{eq:floor}}
\newcommand{\abs}[1]{\linkedBrac[\normalcolor]{|}{#1}{|}{def:absolutValue}}

A working example of my code:

\documentclass[a4paper,11pt]{report}
\usepackage{amsmath}
\usepackage[colorlinks=true,linkcolor=blue]{hyperref}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{definition}[theorem]{Definition}

\newcommand{\BracKern}{\kern-\nulldelimiterspace}%https://tex.stackexchange.com/a/54035/128042

\newcommand{\linkedBrac}[5][]{% #2,#4 = left/right bracket type; #5 = label of link-target; optional argument #1: one can insert something like \color{green} here 
        \mathopen{\hyperref[#5]{#1\left#2\vphantom{#3}\BracKern\right.}}% left bracket
        #3%  content
        \mathclose{\hyperref[#5]{#1\left.\BracKern\vphantom{#3}\right#4}}% right bracket
}%https://tex.stackexchange.com/questions/360507/hyperref-delimiters-brackets-norms-parenthesis-using-left-and-right-suspe

\newcommand{\normOne}[1]{\linkedBrac{\|}{#1}{\|_1}{def:norm1}}
\newcommand{\normTwo}[1]{\linkedBrac{\|}{#1}{\|_2}{def:norm2}}
\newcommand{\floor}[1]{\linkedBrac[\color{green}]{\lfloor}{#1}{\rfloor}{eq:floor}}
\newcommand{\ceil}[1]{\linkedBrac[\color{red}]{\lceil}{#1}{\rceil}{eq:ceil}}
\newcommand{\Sawtooth}[1]{\linkedBrac[\color{yellow}]{\{}{#1}{\}}{eq:Sawtooth}}
\newcommand{\abs}[1]{\linkedBrac[\normalcolor]{|}{#1}{|}{def:absolutValue}}

\begin{document}
\begin{definition}[absolut value]\label{def:absolutValue}
$ \abs{x}=\max (x,-x) $
\end{definition}
\begin{definition}[$\ell_1-Norm$]\label{def:norm1}
\[ \normOne{x} := \sum_{i=1}^{n} \abs{x_i} \]
\end{definition}
\begin{definition}[$\ell_2-Norm$]\label{def:norm2}
\[ \normTwo{x} := \left( \sum_{i=1}^{n} \abs{x_i}^2 \right)^{\frac{1}{2}} \]
\end{definition}
\begin{definition}[floor,ceil,Sawtooth function]
\begin{align}
\floor{x} := \max\lbrace z\in Z | z\leq x \rbrace \label{eq:floor}\\
\ceil{x} :=\min\left\lbrace z\in Z \middle| z\geq x \right\rbrace \label{eq:ceil}\\
\Sawtooth{x} := x - \floor{x} \label{eq:Sawtooth}
\end{align}
\end{definition}

many pages later...

\begin{align}
\normOne{ \floor{ \normTwo{y} - 3 } \hat{A}x}\\
\normOne{ \ceil{ \normTwo{y} - 3 } \hat{A}x}\\
\Sawtooth{\normOne{ \left( \normTwo{y} - 3 \right) \hat{A}x}}
\end{align}
\end{document}

This code producing following result: here is a link to the pdf: http://docdro.id/HZMP7Uy This looks exactly the way I wanted it to look and all links link to the correct position :)

Thanks for this comment by Gustavo Mezzetti that led me in right direction. My solution is based on this post by Peter Grill and this post by egreg

I can think of only one thing that could be improved: When I open move the mouse over a bracket in firefox-build-in-pdf-reader only one bracket gets highlighted. I think it would be absolutely beautiful if moving the mouse over one bracket would result in highlighting both brackets, but I am not sure if this is possible. (If someone can solve this, I will unaccept my solution and accept the more capable solution of course.)