Hello!

Could you please help a bit with this problem?

In the Banach space the sequence of elements is defined by

where is the co-ordinate sequence . Let M be the closed linear span of the elements . By considering the liner functional f on defined by

or otherwise, prove that M does not coincide with .

Now, suppose that , and

and M is as before. Prove that iff s>1 or s<-3.

I have no idea where to start... any hints would be appreciated.