MathProblemsBank

19.3.6 Linear operators

Problem: Prove that the sequence of operators \[ A_{n} x=(\underbrace{0, \ldots, 0}_{n}, x_{1}, \ldots, x_{n}, 0,0, \ldots) \] where \( A_{n}: l_{1} \rightarrow l_{1} \), doesn't converge pointwise to the zero operator.