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  "body": "\n## Summary\n\nThe essential spectrum of a bounded operator is the part of its spectrum that does not change under compact perturbations.\nIt consists of the $\\lambda$ for which $T - \\lambda I$ is not a Fredholm operator.\nFor a self-adjoint operator on a Hilbert space, it is what remains of the spectrum after removing the isolated eigenvalues of finite multiplicity.\n\n## Explanations\n\n### L1 human\n\nSome points of the spectrum are fragile: an isolated eigenvalue with a finite-dimensional eigenspace can be moved or removed by adding an operator of finite rank.\nOther points are robust, because they involve infinitely many directions at once.\nThe essential spectrum collects the robust points.\nFor example, every compact operator on an infinite-dimensional space has essential spectrum $\\set{0}$, and the identity has essential spectrum $\\set{1}$.\n",
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