Spacing between triple vertical lines

Question

I would like to create a norm-like operator with 3 verticals bars instead of two. It has to look like $|||\cdot|||$. I would like to know how to decrease the spacing between the vertical bars such that it has the same spacing as the $\lVert .. \rVert$ command.

There is a command available in the stmaryrd package called \biginterleave, but this command has to much spacing between the vertical bars, especially in display math mode.

Is there some work-around to adjust the spacing between to vertical bars?

Answer 1

Here's a solution that doesn't require the use of additional packages. The new command, \vertiii, takes one argument; the triple vertical bars resize automatically depending on the size of the argument. For the MWE below, I've actually set the spacing between the vertical bars to be slightly less than what's generated by \[l,r]Vert -- you can adjust the spacing to suit your taste by changing the value of the argument of the four \kern commands.

Addendum: I've modified the code -- by inserting curly braces around the entire command -- to allow for the use of the command \vertiii in subscripts and superscripts as well.

\documentclass{article}
\usepackage{amsmath,amssymb}
\newcommand{\vertiii}[1]{{\left\vert\kern-0.25ex\left\vert\kern-0.25ex\left\vert #1 
    \right\vert\kern-0.25ex\right\vert\kern-0.25ex\right\vert}}
\begin{document}
$\vertiii{a}$, 
$\vertiii{\int_0^1 a(x)\,\mathrm{d}x}$,
$\displaystyle \vertiii{\int_0^1 a(x)\,\mathrm{d}x}_\vertiii{b}$

$\lVert a \rVert$ (for comparison)

$c_\vertiii{d}$, $f^\vertiii{g}$
\end{document}

Answer 2

A solution modelled on Mico's, but that allows also for use in subscripts and superscripts. Using \mkern-1.5mu seems better; this should be adjusted if other base fonts are used, comparing to what \| produces.

The syntax is similar to the one used by mathtools for "fenced" symbols:

\opnorm{a}        % normal size
\opnorm[\big]{a}  % slightly larger
\opnorm[\Bigg]{a} % largest
\opnorm*{a}       % \left and \right

Here's the example.

\documentclass{article}
\usepackage{amsmath,amssymb}
\makeatletter
\newcommand{\opnorm}{\@ifstar\@opnorms\@opnorm}
\newcommand{\@opnorms}[1]{%
  \left|\mkern-1.5mu\left|\mkern-1.5mu\left|
   #1
  \right|\mkern-1.5mu\right|\mkern-1.5mu\right|
}
\newcommand{\@opnorm}[2][]{%
  \mathopen{#1|\mkern-1.5mu#1|\mkern-1.5mu#1|}
  #2
  \mathclose{#1|\mkern-1.5mu#1|\mkern-1.5mu#1|}
}
\makeatother

\begin{document}

$\opnorm{a}$,
$\opnorm[\Big]{\int_0^1 a(x)\,\mathrm{d}x}$,
$\displaystyle \opnorm*{\int_0^1 a(x)\,\mathrm{d}x}_{\opnorm{a}}$

$\lVert a \rVert$ (for comparison)

\end{document}

Answer 3

The fourier package provides such a symbol, called \VERT. However, \usepackage{fourier} will change the font throughout your document. You can access just this one symbol by adding its definition (taken from fourier.sty) to your preamble.

\documentclass{article}
\DeclareFontEncoding{FMS}{}{}
\DeclareFontSubstitution{FMS}{futm}{m}{n}
\DeclareFontEncoding{FMX}{}{}
\DeclareFontSubstitution{FMX}{futm}{m}{n}
\DeclareSymbolFont{fouriersymbols}{FMS}{futm}{m}{n}
\DeclareSymbolFont{fourierlargesymbols}{FMX}{futm}{m}{n}
\DeclareMathDelimiter{\VERT}{\mathord}{fouriersymbols}{152}{fourierlargesymbols}{147}
\begin{document}
The quick brown fox jumps over the lazy dog.
\[ 
\VERT x \VERT \quad \left\VERT\frac{1}{2}\right\VERT 
\]
\end{document}

Answer 4

A solution using \vvvert of package mathabx. The symbol can also be used with \left and \right. Since the package changes many math symbols, the following example only defines \vvvert and the symbol fonts, needed for it without changing other math symbols:

\documentclass{article}
%\usepackage{mathabx}

% Math symbol font matha
\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
      <5> <6> <7> <8> <9> <10> gen * matha
      <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
      }{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}
\DeclareFontSubstitution{U}{matha}{m}{n}

% Math symbol font mathb
\DeclareFontFamily{U}{mathx}{\hyphenchar\font45}
\DeclareFontShape{U}{mathx}{m}{n}{
      <5> <6> <7> <8> <9> <10>
      <10.95> <12> <14.4> <17.28> <20.74> <24.88>
      mathx10
      }{}
\DeclareSymbolFont{mathx}{U}{mathx}{m}{n}
\DeclareFontSubstitution{U}{mathx}{m}{n}

% Symbol definition
\DeclareMathDelimiter{\vvvert}{0}{matha}{"7E}{mathx}{"17}

\begin{document}
\[
  \left\vvvert \frac{A}{B}\right\vvvert
\]
\end{document}