Dear Colleagues,

Could you please help me in solving the following problem:

Show that $\displaystyle Y=\{x| \ x=(x_{j})\in \ell^{2}, x_{2n}=0, n=1,2,3,...\}$ is a closed subspace of $\displaystyle \ell^{2}$ and find $\displaystyle Y^{\bot}$.

What is $\displaystyle Y^{\bot}$ if $\displaystyle Y=span\{e_{1},...,e_{n}\}\subset \ell^{2}$, where $\displaystyle e_{j}=(\delta _{jk})$?

Regards,

Raed.