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Thread: Right shift operator

  1. #1
    Sep 2009

    Right shift operator

    Dear Colleagues,

    Could you please help me in solving the following problem:
    Let (e_{n}) be a total orthonormal sequence in a separable Hilbert space H and define the right shift operator to be the linear operator T form H into H such that Te_{n}=e_{n+1} for n=1,2,3,..., what is the Hilbert-adjoint operator T^{*} of T.

    Best Regards.
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  2. #2
    Super Member girdav's Avatar
    Jul 2009
    Rouen, France
    What did you try?
    You only have to know the definition of the adjoint of an operator and work with the infinite sum.
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