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

Let an operator over the Hilbert space , we call it *bounded* if there exists a such that , with . The set of all bounded operators over is denoted by . In particular the minimum for which the inequality above holds, is called the *operator norm* of . 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.