Stochastic integral representations of second quantification operators
نویسنده
چکیده
We give a necessary and sufficient condition for the second quantification operator Γ(h) of a bounded operator h on L2 (R+), or for its differential second quantification operator λ(h), to have a representation as a quantum stochastic integral. This condition is exactly that h writes as the sum of a Hilbert-Schmidt operator and a multiplication operator. We then explore several extensions of this result. We also examine the famous counterexample due to Journé and Meyer and explain its representability defect.
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