What is the modern classification of linear operators?
Especially interesting regarding linear operators on numerical functions.
closed as not a real question by Mariano Suárez-Alvarez♦, Jonas Meyer, Andres Caicedo, Arturo Magidin, Mike Spivey Jan 29 '11 at 0:43
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There are any number of classes of linear operators that people are interested in, depending on what situation you are in. Some examples:
If your space comes equipped with an inner product, one has:
For normed spaces you have bounded operators. Etc.
Is this more or less what you are thinking of?