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Thread: 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 $\displaystyle H=L^{2}(0,1)$ that is $\displaystyle Tf(x)=xf(1-x^{3})$ and I want to find $\displaystyle T^{*}$, $\displaystyle T^{*}T$ and $\displaystyle \left \| T \right \|$. 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 $\displaystyle T^*$, remember that a linear functional $\displaystyle l$ in $\displaystyle L^2(0,1)$ is given by a function $\displaystyle g\in L^2(0,1)$: $\displaystyle l(f) = \int_{(0,1)}f(x)g(x)\lambda(dx)$.
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