Right shift operator

• May 11th 2011, 09:39 AM
raed
Right shift operator
Dear Colleagues,

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 $T$.