# A solution for reducing spacing and for a particular superscript with *

Personally I am trying to find, for my book, an optimal solution that allows, using the characters highlighted in my small MWE, to reduce the spacing in mathematical mode between the two symbols (i.e. between A and +, \lambda and *, ecc.) highlighted in the yellow rectangle with the arrows, and to insert the asterisk in a lower position than the basic one (see blue arrow).

I was wondering if the spacing you create between two character is automatic or it is a font problem.

A partial but canonical solution that I have thought could be to insert a negative space \! between a symbol and the other, to reduce the size of the + character using the command \scriptstyle.

Thank you all for your patience and cooperation.

\documentclass{article}
\usepackage[lite]{mtpro2}
\usepackage{amsmath}
\usepackage{newtxtext}
\begin{document}
$\lambda (Au,v)=\lambda(u, A^+v)=(u,\lambda^*A^+v)$
$\overline A_u=\frac{(Au, u)}{(u,u)}=\frac{(u, Au)}{(u,u)}=\overline A^*_u$
\end{document}

• suggestion for the case of asterisk following A with overline: insert an empty group {} before the ^*. (i'm not able to test anything at the moment.) – barbara beeton Nov 22 '18 at 13:12
• For the asterisk, I tested your suggestion. Perfect! I vote + 1. But why does the asterisk go too far up if I don't put the group {} before ^*? – Sebastiano Nov 22 '18 at 13:22
• @Sebastiano because it no longer sees the size of the overline char – daleif Nov 22 '18 at 13:33
• Note it should have said "of the overlined char", {}  is an empty atom and as such has a certain size of its own. I often make my own overline macro (named by the actual mathematical meaning of overline in this case), this macro will overline the contents, but it will also leave a height that is the same as the input. Note for example that Barbara's suggestion might not work well with an a. My macro is just implemented by adding a vphantom at the end – daleif Nov 22 '18 at 16:23
• The asterisk would not be too high with \bar{A}_u^*, which I recommend over \overline. And no, the \bar accent is not too short. – egreg Nov 22 '18 at 20:51

## 1 Answer

TeX needs sometimes help when adjacent symbols have “incompatible shapes”.

This is the case for \lambda^*, where the asterisk is printed a bit too far; the same happens to me when I need \mathbf{A}^{T} to denote the transpose, but not with \mathbf{B}^T.

The solution here is to do a small backspacing in the exponent, so \lambda^{\!*} to compensate for the hole.

The asterisk is raised with \overline{A}^* because \overline{A} is a single Over atom and the whole height is considered. To the contrary, TeX just considers the height of the nucleus for an Acc atom such as \bar{A}.

In general, \bar is better than \overline, for a single symbol, much less intrusive. If you insist on \overline, then adding an empty group after the symbol might help, but it would inhibit the kerning of the subscript as shown in the example below.

\documentclass{article}
\usepackage{newtxtext}
\usepackage[lite]{mtpro2}
\usepackage{amsmath}
\begin{document}

$\mathbf{A}^T\mathbf{B}^T \qquad \mathbf{A}^{\!T}\mathbf{B}^T$

$\lambda (Au,v)=\lambda(u, A^+v)=(u,\lambda^{\!*}A^+v)$

$\bar{A}_u=\frac{(Au, u)}{(u,u)}=\frac{(u, Au)}{(u,u)}=\bar{A}^*_u$

$\overline{A}_u=\frac{(Au, u)}{(u,u)}=\frac{(u, Au)}{(u,u)}=\overline{A}{}^*_u$

$\overline{P}{}_u^* \qquad \bar{P}_u^*$

\end{document}