19.3.21 Linear operators

Condition: Determine under what conditions \( \left(\lambda_{1}, \lambda_{2}, \ldots\right) \) the operator \( A: l_{2} \rightarrow l_{2}, \quad A\left(x_{1}, x_{2}, \ldots\right)=\left(\lambda_{1} x_{1}, \lambda_{2} x_{2}, \ldots\right) \) is bounded, and find its norm in this case.