nuclear space
C60606
concept
A nuclear space is a topological vector space in which every continuous linear map into an arbitrary Banach space is nuclear (i.e., can be approximated by finite-rank operators with rapidly decaying singular values), giving it strong compactness and approximation properties.
All labels observed (2)
| Label | Occurrences |
|---|---|
| nuclear space canonical | 2 |
| Montel space | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: nuclear space
Generated description
A nuclear space is a topological vector space in which every continuous linear map into an arbitrary Banach space is nuclear (i.e., can be approximated by finite-rank operators with rapidly decaying singular values), giving it strong compactness and approximation properties.
Instances (2)
| Instance | Via concept surface |
|---|---|
| Schwartz–Bruhat space | — |
| Schwartz space | — |