##  [Trace-Class Operator](/trace-class-operator) 

  ##  [Trace-Class Operator](https://natural.quantumdictionary.io/trace-class-operator-0) 

  

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Definition

On a Hilbert space, a trace-class operator is a compact operator whose singular values are summable; such operators admit a well-defined trace equal to the sum of diagonal entries in any orthonormal basis and a well-defined determinant (Fredholm determinant) in some contexts.