You made couple of bugs here.
The problem with invalid "Files" here is simply related to the
blank space in "Program Files". You should enclose the file name in this directory in "". But don't do it, just yet, first fix another bug (but both problems are good to understand).
The second bug is:
you absolutely don't need "cmd.exe". Who told you it should be there? This is just yet another program, a command interpreter, it does nothing special compared to your, as the starting of the process is concerned. In other words, you need only the application file "takeown".
Do this:
string fileName =
string application = "takeown";
string arguments = string.Format(@"/f ""{0}""", fileName);
System.Diagnostics.Process.Start(application, arguments);
Now, about running as administrator. You should better request elevated privileges for the application running this code. You can do it with the application manifest. I explain this problem in detain via references in my recent answer:
Get rights for my WPF application[
^].
That's all you need to resolve your problem. By the way, I doubt making ownership of the file like the one you show makes sense. Why? Just a note not related to your question itself.
—SA