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  "body": "\n## Summary\n\nA Hankel operator is a bounded operator on $\\ell^2$ whose matrix $(a_{j+k})_{j,k \\ge 0}$ is constant along each anti-diagonal, an infinite [[Hankel matrix|PQ1D8FQB3E]].\nUp to a unitary identification of the spaces, the same operators arise in a function form.\nThey are the maps $f \\mapsto (I - P)(\\varphi f)$ from the [[Hardy space|PNNNFJVF6W]] $H^2$ to $L^2 \\ominus H^2$ on the circle.\nHere $\\varphi$ is a bounded symbol and $P$ is the projection onto $H^2$.\nHankel operators are close relatives of [[Toeplitz operators|GQ0X3R3WM2]] and appear in rational approximation, control theory and prediction theory.\nNehari's theorem describes the bounded ones, and Kronecker's theorem the ones of finite rank.\n\n## Explanations\n\n### L1 human\n\nA Hankel matrix has the same entry along every line that runs from the lower left to the upper right.\nSo the whole matrix is built from one sequence $a_0, a_1, a_2, \\ldots$, with $a_{j+k}$ in row $j$ and column $k$.\nThe Hilbert matrix, with entries $1/(j + k + 1)$, is the classical example.\nThe operator theory question is which sequences give a bounded operator on square-summable sequences.\n",
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