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    A proof that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H

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    Prove that for any self-adjoint bounded linear operator T on a Hilbert space H that

    (Tf,f)

    is real-valued for all f in H.

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    https://brainmass.com/math/matrices/proof-self-adjoint-linear-operator-5497

    Solution Preview

    Recall that if T:H to H is a bounded linear operator on the Hilbert space H then there
    exists a unique and bounded linear operator T^* such that

    T^* : H to H

    and for all g ...

    Solution Summary

    It is proven that for a self adjoint linear operator T, (Tf,f) is real for all f in the Hilbert space H, where (f,f) denotes the inner product on H.
    The solution is detailed and well presented.

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