Turning a T1 text-mode character into a maths-mode character

Question

I would like to use the T1 font character Ð, \DH, as a mathematical symbol, as so in a quick and dirty way I defined

\newcommand{\dH}{\text{\DH}}

However, in my theorem environments, where the default is italic text, the Ð is italicised, which is not the case for my equation symbols which are standard roman characters. For instance,

\begin{lemma}\label{depth_bounds}
The depth function $\dH_{Y'}$ satisfies the inequalities
\[
\dH_{Y'}(x,y) \le lcm(\dH_{G/K}(x),\dH_Y(y))
\]
\end{lemma}

The disparity with \dH_Y outside the lemma environment, for example, is blatantly obvious: Ð_Y vs Ð_Y, modulo HTML spacing issues.

Answer 1

So for the actually intended way you want to use it, here’s your solution:

\newcommand{\dH}{\text{\normalfont\DH}}

This should print the \DH in “upright character” while the rest of the lemma is italic, as it’s supposed to be.

Answer 2

I’m not 100% sure whether I got your question right, to be honest, but here is my attempt.

This:

\documentclass[paper=a4, fontsize=11pt]{article} 

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc} 

\usepackage{amsmath, amsthm, amssymb}

\newcommand{\dH}{\text{\DH}}

\begin{document}

\newtheorem{lem}{Lemma}
Lemma environment:
\begin{lem}\label{depth_bounds}
The depth function $\dH_{Y'}$ satisfies the inequalities
\[
\dH_{Y'}(x,y) \le lcm(\dH_{G/K}(x),\dH_Y(y))
\]
\end{lem}

Equation environment:
\[
\dH_{Y'}(x,y) \le lcm(\dH_{G/K}(x),\dH_Y(y))
\]
\end{document}

results in

While a small change – namely: \newcommand{\dH}{\text{\itshape\DH}}– results in: