Now use twenty minutes to explain why we consider Hilbert Schmidt operator on Hilbert probability space.

We consider an operator where is a Hilbert space with probability measure . Then when is Hilbert Schmidt, let’s denote where , then we have

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Now use twenty minutes to explain why we consider Hilbert Schmidt operator on Hilbert probability space.

We consider an operator where is a Hilbert space with probability measure . Then when is Hilbert Schmidt, let’s denote where , then we have