Dear Colleagues,

Could you please help me in solving the following problem:

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

Regards,

Raed.