##  [Compact Operator](/compact-operator) 

  ##  [Compact Operator](https://natural.quantumdictionary.io/compact-operator-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A linear operator between Banach (or normed) spaces that maps bounded sets to relatively compact sets — equivalently, the image of the unit ball has compact closure.

 

 

 

 

 





 

 



 ##  [Compact Operator](https://puremath.quantumdictionary.io/compact-operator-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A linear operator between topological (often normed or Banach) vector spaces that maps bounded sets to relatively compact sets; equivalently, the image of any bounded sequence has a convergent subsequence in the target space.