# Thread: Right shift operator

1. ## 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.

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