Bounded Operator

Overview


Given two normed vector spaces {% X %} and {% Y %}, a bounded operator is an operator
{% T: X \rightarrow Y %}
such that there exists a {% K \geq 0 %}
{% || T(x) || \leq K || x || %}

Set of Bounded Operators


The set of bounded operators on a Hilbert Space {% \mathcal{H} %} is typically denoted {% B(\mathcal{H}) %}