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Is it possible to get italic correction work in math mode?
I found that F or C followed by a \forall extremely ugly in TeX/LaTeX, and
inserting \/ like F \/ \forall does not help.
Is F \, \forall the recommended solution? Or is it possible to use a mechanism
similar to italic correction in text mode?
As mentioned in comments, there is no italic correction in math-mode. There may be fonts which provide a better kerning in this case and of course, you could ask the maintainer of your font to include kerning pairs for C\forall and F\forall.
But actually I would not recommend that as it gets difficult to read if set too close together. I would treat \forall like a real word and therefore write something like $C\ \forall\ x$.
If you want to have some special kerning different to your proposed \, you might use my following MWE. Of course, you could define macros for often used combinations (\newcommand*{\Cforall}{C\,\forall}) or define your own \forall (\newcommand*{\myForall}{\,\forall\,}). The last option is quite similar to what the command \in is producing...
% arara: pdflatex
\documentclass{article}
\begin{document}
\noindent
$C\forall x$\\
$C\,\forall\,x$\\
$C\mkern4mu\forall\mkern4mu x$\\
$C\ \forall\ x$
\end{document}
$f$is not italics. Also,\forallis just a symbol that translates tofor allrather than it being an operator that acts on certain operands (left and/or right). So, the spacing is ultimately up to you.\forallis not an operator, but the F touches the\forallthat follows, which I found ugly.\forallafter a comma and a space, the space is usually a normal space\or a\enskip(half of an\quad) in inline math and a full\quadin display math. E.g.,$\forall x \in \mathbb{C}, \enskip \exists \alpha_0 > 1$.