Examples
- For some fixed g ∈ C(R), define the linear operator T by
- That the operator T is indeed compact follows from the Ascoli theorem.
- More generally, if Ω is any domain in Rn and the integral kernel k : Ω × Ω → R is a Hilbert—Schmidt kernel, then the operator T on L2(Ω; R) defined by
- is a compact operator.
- By Riesz's lemma, the identity operator is a compact operator if and only if the space is finite dimensional.
Read more about this topic: Compact Operator
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