Neumann series in Banach algebras

The Neumann series can be generalized to a Banach algebraMathworldPlanetmath 𝒜 with identity elementMathworldPlanetmath e. Thus we have:

If x𝒜 is such that x<1 then e-x is invertiblePlanetmathPlanetmath with inverseMathworldPlanetmathPlanetmathPlanetmath given by



Title Neumann series in Banach algebras
Canonical name NeumannSeriesInBanachAlgebras
Date of creation 2013-03-22 17:23:19
Last modified on 2013-03-22 17:23:19
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 4
Author asteroid (17536)
Entry type Theorem
Classification msc 46H05