Then

In these notes we provide an introduction to compact linear operators on Banach and Hilbert spaces. These operatorsbehave very much likefamiliar finite dimensional matrices, without necessarily having finite rank. For more thorough treatments, see [RS, Y]. Definition 1 Let X and Y be Banach spaces. A linear operator C: X → Y is said to be compact if for each bounded sequence {xi}i∈IN ⊂ X, there is a subsequence of {Cxi}i∈IN that is convergent. Example 2 Let a < b and c < d. If C: [c,d]×[a,b] → C is continuous, then the integral operato