Everything here is in a Hilbert space. If [itex]x_n\to x[/itex] and [itex]y_n\to y[/itex] in norm, then under what conditions does(adsbygoogle = window.adsbygoogle || []).push({});

[itex]<x_n,y_n>\to <x,y>[/itex]?

Is this always true, and why?

Does anyone have a source?

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# Interchaning Limits and Inner Products

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