Precisely, given an example of nets of operators $(T_\lambda) , (S_\lambda) \in \mathcal{B} (\mathcal{H}) $, $\mathcal{H} $ being a Hilbert space, converging respectively to $T, S $ in the strong operator topology, but the net $(T_\lambda S_\lambda) $ does not converge to $TS$ (in the same topology of course)
2026-04-12 13:31:37.1776000697
What are examples of operators showing that convergence in the strong operator topology doesn't behave well?
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