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

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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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