##  [Nuclear Space](/nuclear-space) 

  ##  [Nuclear Space](https://puremath.quantumdictionary.io/nuclear-space-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A locally convex topological vector space with the property that continuous linear maps from it to arbitrary Banach spaces factor in a way analogous to trace-class (nuclear) operators: bounded sets map to relatively compact sets under appropriately approximating finite-rank factorizations, yielding strong compactness and tensor-product regularity.