Cfrtjryk

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

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:

The answer of @Kurt 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}

    ifxinserttheoremaddition@emptyelse inserttheoremadditionfi%

  }%

}

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}