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  "body": "\n## Summary\n\nA strictly singular operator is a bounded linear map between Banach spaces that is not an isomorphism on any infinite-dimensional closed subspace.\nEvery compact operator is strictly singular, but the converse fails in general Banach spaces.\nStrictly singular operators share an important property with compact ones: adding one of them to a Fredholm operator does not change the Fredholm index.\n\n## Explanations\n\n### L1 human\n\nAn isomorphism onto its image keeps every vector at a length comparable to its original length.\nA strictly singular operator cannot do that on any infinite-dimensional piece of the space: on every such piece some unit vectors are shrunk almost to zero.\nFor example, the inclusion of the sequence space $\\ell^1$ into $\\ell^2$ is strictly singular.\nIt is not compact, since it sends the unit vectors $e_n$ to unit vectors at distance $\\sqrt{2}$ from each other.\n",
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