multiplication operator on L2

Let (X,𝒜,μ) be a measure spaceMathworldPlanetmath and f:X𝕂 a measurable functionMathworldPlanetmath. Then Mf:ϕfϕ is the multiplication operator with f defined on the subspacePlanetmathPlanetmath Dom(Mf)={ϕL𝕂2(X,𝒜,μ):fϕL𝕂2(X,𝒜,μ)}. It plays an important role in quantum mechanics where the multiplicationPlanetmathPlanetmath with the coordinates on n is the position operator.

Title multiplication operator on L2
Canonical name MultiplicationOperatorOnL2
Date of creation 2013-03-22 15:42:28
Last modified on 2013-03-22 15:42:28
Owner scineram (4030)
Last modified by scineram (4030)
Numerical id 8
Author scineram (4030)
Entry type Definition
Classification msc 47B38
Related topic operator
Defines multiplication operator