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
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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