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Math Help - Closed linear span of subspace

  1. #1
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    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.
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  2. #2
    Senior Member Shanks's Avatar
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    Quote Originally Posted by KSM08 View Post
    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 ?
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  3. #3
    Senior Member Shanks's Avatar
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    One more question

    The definition of the convergence in X is not clear, can you write it down here ?
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