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Math Help - Right shift operator

  1. #1
    Member
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    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
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    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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