# Orthogonal Complement 2

• Apr 1st 2011, 01:19 PM
raed
Orthogonal Complement 2
Dear Colleagues,

If $M\neq \phi$ is any subset of a Hilbert space $H$, show that $M^{\bot\bot}$ is the smallest closed subspace of $H$ which contains M, that is, $M^{\bot\bot}$ is contained in any closed subspace $Y\subset H$ such that $Y\supset M$.

Regards,

Raed.
• Apr 1st 2011, 01:23 PM
girdav
What did you try ?
• Apr 1st 2011, 02:12 PM
raed
Give me a hint please and I will then continue.
• Apr 7th 2011, 07:15 PM
mr fantastic
Quote:

Originally Posted by raed
Give me a hint please and I will then continue.

No, that's not how it works.

What have you tried? Where are you stuck? You have to make an effort.