nuclear space

If E is a Fréchet space and (pj) an increasing sequence of semi-norms on E defining the topology of E, we have


where E^pj is the Hausdorff completion of (E,pj) and E^pj+1E^pj the canonical morphism. Here E^pj is a Banach spaceMathworldPlanetmath for the induced normPlanetmathPlanetmath p^j.

A Fréchet space E is said to be nuclear if the topology of E can be defined by an increasing sequence of semi-norms pj such that each canonical morphism E^pj+1E^pj of Banach spaces is nuclear.

Recall that a morphism f:EF of completePlanetmathPlanetmathPlanetmath locally convex spaces is said to be nuclear if f can be written as


where (λj) is a sequence of scalars with |λj|<+,ξjE an equicontinuous sequence of linear forms and yjF a boundedPlanetmathPlanetmath sequence.

Title nuclear space
Canonical name NuclearSpace
Date of creation 2013-03-22 16:37:28
Last modified on 2013-03-22 16:37:28
Owner Simone (5904)
Last modified by Simone (5904)
Numerical id 6
Author Simone (5904)
Entry type Definition
Classification msc 46B20