Use the \mathop command, as in:
\newcommand{\diag}{\mathop{\mathrm{diag}}}
Subscripts and superscripts on \diag will be placed as they are on
\lim. If you want your subscripts and superscripts always placed
to the right, do:
\newcommand{\diag}{\mathop{\mathrm{diag}}\nolimits}
AMSLaTeX (in its amsopn package) provides a command
\DeclareMathOperator that takes does the same job as the first
definition above. To create our original \diag command, one would
say:
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator* declares the operator always to have its
sub- and superscripts in the
"\limits position".
(It should be noted that "log-like" was reportedly a joke on Lamport's part; it is of course clear what was meant.)
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