This is a special class of operators and for several reasons it is good to study them in some detail at this stage. Their spectral theory is much simpler than that of general bounded operators, and it is just a little bit more complicated than that of finite-dimensional operators. Many problems in mathematical physics lead to integral equations, and the associated integral operators are compact. For this reason these operators were among the first to be studied, and in fact, this was the forerunner to the general theory.
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