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Math Help - About a multiplication operator

  1. #1
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    About a multiplication operator

    I have stuck on a problem on Linear operators... Could anybody help me?
    I have a linear operator in a Hilbert Space H=L^{2}(0,1) that is Tf(x)=xf(1-x^{3}) and I want to find T^{*}, T^{*}T and \left \| T \right \|. What should I do?
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  2. #2
    Super Member girdav's Avatar
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    Re: About a multiplication operator

    To find T^*, remember that a linear functional l in L^2(0,1) is given by a function g\in L^2(0,1): l(f) = \int_{(0,1)}f(x)g(x)\lambda(dx).
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