Orthogonal projection.

Asked Nov 24 '13 at 00:39

Active Nov 24 '13 at 01:11

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I have found this question in a book, but I don't know how to use that $\left\Vert P\right\Vert =1$.

Question: If $P\in\mathcal{L}(H)$ is a projection and $\left\Vert P\right\Vert =1$, show that $P$ is an orthogonal projection.

Where $\mathcal{L}(H)$ is the set of linear bounded operators on a Hilbert space $H$.

Thanks.

asked Nov 24 '13 at 00:39

1

It's a classical exercise. – Julien Nov 24 '13 at 00:50
@AndrésFelipeTéllezCrespo: Suggestion: to get good answers, why don't you explain first what have you done so far to try to solve the problem? Did you write down the definition of orthogonal projection? – Sergio Parreiras Nov 24 '13 at 01:02

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