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.