= Hellinger–Toeplitz theorem
{wiki=Hellinger–Toeplitz_theorem}
The Hellinger–Toeplitz theorem is a result in functional analysis that characterizes certain types of operators, specifically compact operators on Hilbert spaces. It states that if \\( T \\) is a compact linear operator on a Hilbert space \\( H \\), then the following conditions are equivalent: 1. \\( T \\) is a compact operator. 2. The image under \\( T \\) of the unit ball in \\( H \\) is relatively compact in \\( H \\) (i.
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