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  "body": "\n## Summary\n\nA hyponormal operator is a bounded operator $T$ on a Hilbert space with $T^*T - TT^* \\ge 0$, equivalently $\\norm{T^*x} \\le \\norm{Tx}$ for all $x$.\nThe class contains the normal operators and the [[subnormal operators|81MZ023K1A]], and it is strictly larger than both.\nHyponormal operators share several properties of normal operators: for instance, the norm equals the spectral radius.\n\n## Explanations\n\n### L1 human\n\nFor a normal operator, $T$ and its adjoint stretch every vector by the same amount.\nA hyponormal operator only requires that the adjoint stretches no vector more than $T$ does.\nThe unilateral shift on sequences is an example: it keeps every length, while its adjoint, the backward shift, shortens the vector $(1, 0, 0, \\ldots)$ to $0$.\n",
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