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Let \Delta an operator over the Hilbert space \mathcal{H}, we call it bounded if and only if ||\Delta |\psi \rangle||\leq  t|||\psi \rangle|| \ \ \forall t \geq 0 \ \ \forall |\psi \rangle \in \mathcal{H}, with |||\psi\rangle||=\sqrt{\langle \psi | \psi \rangle}. The set of all bounded operators over \mathcal{H} is denoted as \mathcal{B}(\mathcal{H}). In particular the minimum t for which the inequality above holds, is called the operator norm of \Delta. This norm induces the operator norm topology. Such norm is typically too strong for many purposes, a very wide used one is the so called weak operator topology, it will be discussed later.