Properties
- If A is a trace-class operator.
- defines an entire function such that
- The function det(I + A) is continuous on trace-class operators, with
One can improve this inequality slightly to the following, as noted in Chapter 5 of Simon:
- If A and B are trace-class then
- The function det defines a homomorphism of G into the multiplicative group C* of non-zero complex numbers.
- If T is in G and X is invertible,
- If A is trace-class, then
Read more about this topic: Fredholm Determinant
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