nuclear space
If is a Fréchet space and an increasing sequence of semi-norms on defining the topology of , we have
where is the Hausdorff completion of and the canonical morphism. Here is a Banach space for the induced norm .
A Fréchet space is said to be nuclear if the topology of can be defined by an increasing sequence of semi-norms such that each canonical morphism of Banach spaces is nuclear.
Recall that a morphism of complete locally convex spaces is said to be nuclear if can be written as
where is a sequence of scalars with , an equicontinuous sequence of linear forms and a bounded sequence.
Title | nuclear space |
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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 |