I've now encountered two different definitions for a projection.(adsbygoogle = window.adsbygoogle || []).push({});

Let X be a Banach space. An operator P on it is a projection if P^2=P.

Let H be a Hilbert space. An operator P on it is a projection if P^2=P and if P is self-adjoint.

But the Hilbert space is also a Banach space, and there's two different definitions for projections then. Are these common definitions anyway?

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# Projections on Banach and Hilbert spaces

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