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  "body": "\n## Summary\n\nA nuclear operator is a bounded linear map between Banach spaces that can be written as an absolutely summable series of rank-one maps.\nThe notion, due to Grothendieck, extends the trace class operators of Hilbert spaces to Banach spaces.\nNuclear operators are compact, and they are the basis of Grothendieck's theory of nuclear spaces and of trace and determinant theory on Banach spaces.\n\n## Explanations\n\n### L1 human\n\nThe simplest operators are those of rank one: measure a vector by a linear functional, then multiply a fixed vector by the result.\nA nuclear operator is an infinite sum of such pieces whose sizes add up to a finite number.\nSo it is a limit of matrices in a strong, summable sense.\nFor example, on square-summable sequences, multiplying the $n$-th coordinate by $2^{-n}$ is nuclear, since it is the sum of the rank-one pieces $x \\mapsto 2^{-n} x_n e_n$ of sizes $2^{-n}$.\n",
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