Dear Colleagues,

Could you please help me in solving the following problem:

Let $\displaystyle (e_{n})$ be a total orthonormal sequence in a separable Hilbert space $\displaystyle H$ and define theright shift operatorto be the linear operator $\displaystyle T$ form $\displaystyle H$ into $\displaystyle H$ such that $\displaystyle Te_{n}=e_{n+1}$ for $\displaystyle n=1,2,3,...$, what is the Hilbert-adjoint operator $\displaystyle T^{*}$ of $\displaystyle T$.

Best Regards.