What is the modern classification of linear operators?
Especially interesting regarding linear operators on numerical functions.
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It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.
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?
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