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## fa.functional analysis – Operators for which operator norm is well-known

let $$T:L^2([0,1])\rightarrow L^2([0,1])$$ be a linear operator of the form
$$T(f):=\int_0^1 \, f(u)\kappa(u,\cdot)du,$$
where $$\kappa:\mathbb{R}^2\rightarrow \mathbb{R}$$ is a continuous function. Is there a class of $$\kappa$$ for the operator norm of $$T$$ is known and is expressed explicitly in terms of $$\kappa$$?

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