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Discussion :: GATE Mathematics

  1. Let c00 be the vector space of all complex sequences having finitely many non-zero terms. Equip c00 the inner product 〈x, y〉 = for all x=(xn) and y=(yn) in c00. Define f: c00 → â„‚ by f(x)= . Let N be the kernel of f.
    Which of the following is FALSE?
    2. A.
    c00 ≠ N
    B.
    N is closed
    C.
    c00 is not a complete inner product space
    D.
    c00 = N ⊕ N⊥

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    Workspace

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    Answer : Option D

    Explanation :

    -NA-

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