Change font of math operators to fontspec font

Question

I'm trying to change the font of math operators (\sin, \limsup, etc.) to Adobe Garamond Pro, which I'm loading via fontspec for use with LuaTeX. I've tried modifying this code by egreg as follows:

\documentclass[letter]{article}
\usepackage{fontspec}
\setmainfont{Adobe Garamond Pro}

% egreg code
\DeclareSymbolFont{garamondOperators}{OT1}{"Adobe Garamond Pro"}{m}{n}
\SetSymbolFont{garamondOperators}{bold}{OT1}{"Adobe Garamond Pro"}{b}{n}

\makeatletter
\renewcommand{\operator@font}{\mathgroup\symgaramondOperators}
\makeatother

% Test code
\begin{document}
$\sup$

sup
\end{document}

The math operators display in Computer Modern even when I enclose the font name with quotation marks. Do I need to import Adobe Garamond Pro and assign it its own name within the preamble in order for it to be recognizable by \DeclareSymbolFont?

EDIT: It turns out that the problem was caused by my use of lmodern in conjunction with fontspec. Without lmodern, everything works flawlessly.

Answer 1

You need no special code:

\documentclass{article}
\usepackage{fontspec}
\setmainfont{Futura} % a very distinctive one

\begin{document}

Math: $\sup$

Text: sup

\end{document}

I changed the font because I don't have Adobe Garamond Pro, but it's the same.