Notation for image and kernel capitalization of first letter

Question

In the mathematical notation for image and kernel one usually writes $\ker$ for kernel and $\DeclareMathOperator{\img}{Im}\img$ for image. Why is the "k" small but the "I" big?

Answer 1

CW answer summing up comments, to push it from unanswered queue:

There is no uniform notation. It may or may not be capitalised.