# Closed linear span of subspace

• Nov 16th 2009, 10:56 AM
KSM08
Closed linear span of subspace
Let X be l infinity, consisting of complex sequences (bj) converging to 1/2b1. Let Y be the subset of X consisting of the sequences e1, e2,... together with the element y=e1 + 1/2(sum over k from 2 to infinity)ek. Show that the closed linear span coincides with X...

Many thanks, in advance.
• Nov 18th 2009, 04:27 AM
Shanks
Quote:

Originally Posted by KSM08
Let X be l infinity, consisting of complex sequences (bj) converging to 1/2b1. Let Y be the subset of X consisting of the sequences e1, e2,... together with the element y=e1 + 1/2(sum over k from 2 to infinity)ek. Show that the closed linear span coincides with X...

Many thanks, in advance.

Do you mean that :the set X is the collection of all infinite complex number sequences which converging to the half of the first term ? and Y is a subset of X consisting of the sequences $e_1,e_2,...$ together with the sequence $e=e_1+\frac {1}{2}\sum_{k=2}^{\infty}e_k$ ?
• Nov 18th 2009, 04:39 AM
Shanks
One more question
The definition of the convergence in X is not clear, can you write it down here ?