I'm trying to familiarize myself with linear operators. In finite dimensions it is clear to me that they are matrices. No problem there. But then in infinite dimensions matters are not so clear to me. Of course the identity map is a linear operator. I also know that if the domain is a space of functions then the integration and differentiation operators are examples of linear operators. Furthermore I found the example of the shift operator (works on sequences and function spaces). But I feel that a few more examples would help me greatly in understanding linear operators better.
Now other than the ones I mentioned what are examples of linear operators $T: X \to Y$ where $X,Y$ are infinite dimensional normed linear spaces?