examples of bounded and unbounded operators

The aim of this page is to list examples of bounded (http://planetmath.org/BoundedOperator) and unbounded linear operatorsMathworldPlanetmath.


  • Shift operators on p

  • A linear operator is continuousMathworldPlanetmath if and only if it is bounded (see this page (http://planetmath.org/ContinuousLinearMapping)).

  • Any isometry is bounded.

  • A multiplication operator h(t)f(t)h(t), where f(t) is continuous and hLp[0,1].

  • An integral operator h(t)01K(t,s)h(s)𝑑s, where 0101|K(s,t)|2𝑑s𝑑t< and hL2[0,1]. In fact this is a Hilbert-Schmidt operator.

  • The Volterra operator h(t)0th(s)𝑑s, where hLp[0,1].


Title examples of bounded and unbounded operators
Canonical name ExamplesOfBoundedAndUnboundedOperators
Date of creation 2013-03-22 15:17:37
Last modified on 2013-03-22 15:17:37
Owner matte (1858)
Last modified by matte (1858)
Numerical id 12
Author matte (1858)
Entry type Example
Classification msc 47L25