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Math Help - Orthogonal Complement 2

  1. #1
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    Orthogonal Complement 2

    Dear Colleagues,

    Could you please help me in solving the following problem:
    If M\neq \phi is any subset of a Hilbert space H, show that M^{\bot\bot} is the smallest closed subspace of H which contains M, that is, M^{\bot\bot} is contained in any closed subspace Y\subset H such that Y\supset M.


    Regards,

    Raed.
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  2. #2
    Super Member girdav's Avatar
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    What did you try ?
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  3. #3
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    Give me a hint please and I will then continue.
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  4. #4
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    mr fantastic's Avatar
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    Quote Originally Posted by raed View Post
    Give me a hint please and I will then continue.
    No, that's not how it works.

    What have you tried? Where are you stuck? You have to make an effort.
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