MathProblemsBank

19.3.3 Linear operators

Problem: Find the spectrum of the operator \( A: l_{2} \rightarrow l_{2} \), \( A\left(x_{1}, x_{2}, \ldots, x_{n}, \ldots\right)=\left(x_{1}, 0, x_{2}, 0, \ldots, x_{n}, 0, \ldots\right) \).