Reading note: A bounded operator approach to Tomita-Takesaki Theory (Rieffel, van Daele)

Let $\mathcal{H}$ be a real Hilbert space. We consider pairs $(\mathcal{K}, \mathcal{L})$ of closed subspaces of $\mathcal{H}$ satisfying the following properties: $\mathcal{K} \cap \mathcal{L} = \{0\}$ and $\mathcal{K} + \mathcal{L}$ is dense in $\mathcal{H}$.

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