Let $H$ be a Hilbert Space, and $M$ a closed subspace. Is it true that
$H = M \bigoplus M^{\perp}$
Does this hold if $M$ is not closed? Or only if $H$ is finite/infinite dimensional?
Let $H$ be a Hilbert Space, and $M$ a closed subspace. Is it true that
$H = M \bigoplus M^{\perp}$
Does this hold if $M$ is not closed? Or only if $H$ is finite/infinite dimensional?
Yes, this is true. Here's how you can go about proving this: