How to make conditional command with non-numerical condition?

Question

I would like to know if someone has a solution to the following problem:

I have recently start to create shortcut to certain operator to display directly the parenthesis around their arguments.

\providecommand{\ker}[1]{\operatorname{ker}\left ( #1 \right )}

for when I want to give the "ker" operator an argument and the command

\providecommand{\Ker}{\operatorname{ker}}

for when I only want to display the operator name.

I would like if there is a way to have those tow command in one such as

\providecommand{\ker}[1][...]{
ifthenelse{...=#1}{
   \operatorname{ker}
}{
   \operatorname{ker} \left ( #1 \right )
}
}

Where ... is the whitespace character \

I would like to avoid to use number in case I have to put them inside or some other characters that could be used to express a vector space.

Thanks to everyone who will take the time to read my question.