Thread: Right shift operator

Dear Colleagues,

Could you please help me in solving the following problem:
Let be a total orthonormal sequence in a separable Hilbert space and define the right shift operator to be the linear operator form into such that for , what is the Hilbert-adjoint operator of .


Best Regards.

What did you try?
You only have to know the definition of the adjoint of an operator and work with the infinite sum.