Write the word 'M$\ddot{\rm u}$ller' in thebibliography

Question

With the following codes

     \documentclass[xcolor=dvipsnames]{beamer}
     \mode<presentation>
      \usetheme{Madrid}
       \begin{document}
      \begin{frame}{}
     \begin{exampleblock}{\textcolor[rgb]{1.00,0.50,0.00}{Theorem} 
      [M$\ddot{\rm u}$ller, Soltysiak (1992)]}
      For a $d$-tuple of ....
     \end{exampleblock}

    \beamertemplatearticlebibitems
    \begin{thebibliography}{10}
     \bibitem{V. Muller, and A. Soltysiak}
    \alert{V. Muller, and A. Soltysiak}
   \newblock  {Spectral radius formula for commuting Hilbert space 
   operators}
   \newblock {\em Studia Math.103. (1992), 329-333}.
     \end{thebibliography}
     \end{frame}
    \end{document}

I get

However I fail to copmilate when I write \bibitem{V. M$\ddot{\rm u}$ller, and A. Soltysiak} \alert{V. M$\ddot{\rm u}$ller, and A. Soltysiak}, and I want to get

Answer 1

Your given code has a missing \end{frame} ...

With using \"u I can compile without errors:

\documentclass[xcolor=dvipsnames]{beamer}

\mode<presentation>
\usetheme{Madrid}

\begin{document}
\begin{frame}{}
     \begin{exampleblock}{\textcolor[rgb]{1.00,0.50,0.00}{Theorem} [M\"uller, Soltysiak (1992)]}
      For a $d$-tuple of ....
     \end{exampleblock}
\end{frame} % <=========================================================

 \begin{frame}
    \beamertemplatearticlebibitems
    \begin{thebibliography}{10}
     \bibitem{V. Muller, and A. Soltysiak}
    \alert{V. M\"uller, and A. Soltysiak} % <===========================
   \newblock  {Spectral radius formula for commuting Hilbert space operators}
   \newblock {\em Studia Math.103. (1992), 329-333}.
     \end{thebibliography}
 \end{frame}
\end{document}

with the result:

Answer 2

The accepted answer already solves your problem with the umlaut. To go one step further use latex's bibliography mechanism and beamer theorem environment and let them do the formatting for you:

\documentclass[xcolor=dvipsnames]{beamer}
\mode<presentation>
\usetheme{Madrid}


\makeatletter
\setbeamertemplate{theorem begin}
{%
    \setbeamercolor{block title}{bg=green!40!black}
  \begin{\inserttheoremblockenv}
  {%
    \textcolor{orange}{\inserttheoremname}
    \ifx\inserttheoremaddition\@empty\else\ \inserttheoremaddition\fi%
  }%
}
\makeatother

\begin{document}
\begin{frame}{}
\begin{theorem}[\cite{MS92}]
For a $d$-tuple of ....
\end{theorem}

\beamertemplatearticlebibitems
\begin{thebibliography}{9}
\bibitem[V. M\"{u}ller and A. Soltysiak (1992)]{MS92}
\alert{V. M\"{u}ller, and A. Soltysiak}
\newblock Spectral radius formula for commuting Hilbert space operators
\newblock \em Studia Math.103. (1992), 329-333.
\end{thebibliography}

\end{frame}
\end{document}