19.3.26 Linear operators

condition: Find the operator conjugate to the operator \( A: l_{1} \rightarrow l_{1} \) if: a) \( A x=\left(x_{1}, \ldots, x_{n}, 0, \ldots\right) \), b) \( A x=\left(\lambda_{1} x_{1}, \lambda_{2} x_{2}, \ldots\right), \quad\left|\lambda_{n}\right| \leq 1 \forall n \), c) \( A x=\left(0, x_{1}, x_{2}, \ldots\right) \), d) \( A x=\left(x_{2}, x_{3}, \ldots\right) \)