It's not clear exactly what layout you want, (perhaps a full minimal example and image in your question would have helped).
The main function of \operatorname
is to provide multi-letter operators like log etc, if you want a math italic f it seems that you just need one of these, depending on where you want the limits to go.
The other function is to give it operator spacing, ie a small gap before the argument, so perhaps the first or second form is what you are looking for?
$ f_1^2 x $
$ \mathop{f_1^2} x $
$ \mathop{{}f}_1^2 x $
$ \mathop{{}f}\limits_1^2 x $
You surely can define your shortcuts; indeed you should.
Let's make some examples. Suppose your document is full of Fourier transforms, for which you need a fancy F. Instead of writing every time
$\mathcal{F}(f)$
it's surely better to define a new command, say
\newcommand{\FT}{\mathcal{F}}
(choose any name you like), so that you can type
$\FT(f)$
and get the same result as before, with a big bonus! If you change your mind about the notation, you can simply modify the definition.
Another example. The "gradient" operator is not predefined; so you might want to have a command for it:
\DeclareMathOperator{\grad}{grad}
A different one; my preferred notation for vectors is, say, \mathbf{v}
. However, since conventions are different, I never type vectors in that way, but prefer to have
\newcommand{\vect}[1]{\mathbf{#1}}
for the same reason as before; I might change my mind and want to modify the appearance, say for using bold italic; this would be accomplished just by saying
\usepackage{bm}
and changing the above into
\newcommand{\vect}[1]{\bm{#1}}
How do you organize this? Here's an example:
\documentclass[a4paper]{book}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc} % input encoding UTF-8
% Useful packages
\usepackage{amsmath,amssymb,amsthm}
% add all the packages you need
% Personal definitions
\newcommand{\FT}{\mathcal{F}} % Fourier transform operator
\DeclareMathOperator{\grad}{grad} % gradient
\newcommand{\vect}[1]{\mathbf{#1}} % vectors and matrices
\begin{document}
...
\end{document}
Add definitions while you find that they are useful for distinguishing logical units of your document.
Best Answer
It's quite strange you refuse loading of other packages: packages good are, says Yoda.
However, if you don't want to use abstract methods and prefer do all the work by hand, you need not even load
amsmath
.