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Math Help - Linear and bounded operator

  1. #1
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    Linear and bounded operator

    Show that
    {f}_{1}(x) = max  x(t) for t\in J, J=[a,b]

     {f}_{2}(x) = min x(t)


    defines functionals on C[a,b]. Are they linear? Bounded?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by kinkong View Post
    Show that
    {f}_{1}(x) = max  x(t) for t\in J, J=[a,b]

     {f}_{2}(x) = min x(t)


    defines functionals on C[a,b]. Are they linear? Bounded?
    What do YOU think?
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  3. #3
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    Quote Originally Posted by Drexel28 View Post
    What do YOU think?
    Help me to get started...
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by kinkong View Post
    Help me to get started...
    Dude, I'm not trying to be a..whatever...but for your own benefit you should at least list your ideas and whatnot.
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  5. #5
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    Quote Originally Posted by Drexel28 View Post
    Dude, I'm not trying to be a..whatever...but for your own benefit you should at least list your ideas and whatnot.
    thanks for the concern...but the problem is i couldnt get started with it...
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  6. #6
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by kinkong View Post
    thanks for the concern...but the problem is i couldnt get started with it...
    Clearly if you get the information about one you get the information about the other since you can just put a minus inside and out and change max to min. For if it's linear, is it true in general that \sup (f+(-f))=\sup(f)+\sup(-f)?
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  7. #7
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    Re: Linear and bounded operator

    i couldnt proceed with this question...i need some help guys..
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  8. #8
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    Re: Linear and bounded operator

    What's the definition of a functional?
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