How to add spacing before and after a cdot?

Question

I'm having the following code:

\documentclass[11pt]{article}
\usepackage{amssymb,amsthm,amsmath}
\newcommand{\norm}[1]{\lVert #1 \rVert_2}

\begin{document}
\begin{displaymath}
\norm{\cdot}=...
\end{displaymath}
\end{document}

I'd like to add a little space before and after the dot in the norm, because it's a bit crushed between the vertical lines now. Is there a command with the same output as \cdot that does this automatically or should I insert the spacing manually (with ~ for example) each time?

Answer 1

I would go even further than Mico, why not embed the empty arg marker into the macro it self.

\documentclass[a4paper]{memoir}
\usepackage{mathtools,etoolbox,amssymb}
\newcommand\emptyarg{{}\cdot{}}
\DeclarePairedDelimiterX\norm[1]\lVert\rVert{
  \ifblank{#1}{\emptyarg}{#1}
}
\begin{document}
\[
\norm{}: A \to B \qquad \norm{X}
\]
\end{document}

BTW: on CTAN the latest mathtools version now contain a tool to build the L^2 norm, such that one does not have to add the _2 manually all the time.

Answer 2

You could define a new macro named, say, "\widecdot", that surrounds \cdot with thinspace (\,) on either side. Note: I wouldn't redefine \cdot directly, as this macro tends to be used internally by other macros as well.

Incidentally, your definition of \norm is a bit suboptimal since subscripts -- such as the 2 in your example -- aren't set quite low enough. It may be preferable to use the macro \DeclarePairedDelimiter of the mathtools package; compare the output of the \norm and \Norm macros in the second equation below.

\documentclass[11pt]{article}
\usepackage{amssymb,mathtools}
\newcommand{\norm}[1]{\lVert #1 \rVert_2}
\DeclarePairedDelimiter{\Norm}{\lVert}{\rVert}
\newcommand\widecdot{\,\cdot\,}
\begin{document}
\[ \norm{\cdot} \text{ vs.\ } \norm{\widecdot}\]

\[ \norm{\widecdot}\text{ vs.\ } \Norm{\widecdot}_2 \]
\end{document}