David Davalos

Mathematical Physicist, Ph.D.

Playing with math sym.

Something interesting must come here soon. This webpage is possible thanks to the support by Armando.

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.

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