In some books, they use a special 'i' for denoting imbedding of one Sobolev space into a another.
This 'i' is not quite like \imath.
It's like a calligraphic 'i'.
I try to find it with detexify, but it doesn't come out.
It looks like this
I'd have thought iota as Michael just said, but your drawing looks more like imath to me
A common notation for imbeddings is the greek