On the geometry of conditional expectations treated as projections on the $L²$-space

Year, pages: 2016, 959 - 966

We study the relative position of two measure-theoretical conditional expectations treated as orthogonal projections on the $L²$-space. We show that any pair of orthogonal projections $P$ and $Q$ on a separable Hilbert space with $\dim(P\wedge Q)=∞$ is unitarily equivalent to the conditional expectations under two sub-$σ$-fields of some probability space.

Komisarski, A., Paszkiewicz, A. 2016. On the geometry of conditional expectations treated as projections on the $L²$-space. In Mathematica Slovaca, vol. 66, no.4, pp. 959-966. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0195

Komisarski, A., Paszkiewicz, A. (2016). On the geometry of conditional expectations treated as projections on the $L²$-space. Mathematica Slovaca, 66(4), 959-966. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0195