ABSTRACT
Suppose {P α } is a family of projections in a von Neumann algebra A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137292/676aa42d-79c8-4246-bc0f-e0fd47650f7d/content/eq1659.tif"/> acting on a Hilbert space H. Let M https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137292/676aa42d-79c8-4246-bc0f-e0fd47650f7d/content/eq1660.tif"/> α be the range of each P α and let M = ⋂ α M https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137292/676aa42d-79c8-4246-bc0f-e0fd47650f7d/content/eq1661.tif"/> α . M is clearly a closed subspace of H. We let Λ α P α denote the orthogonal projection from H onto M; it is the greatest lower bound of {P α }. Let ∨ α P α = I − Λ α ( I − P α ) ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137292/676aa42d-79c8-4246-bc0f-e0fd47650f7d/content/eq1662.tif"/>
