ABSTRACT
Recall that an element x in a C*-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/eq1247.tif"/> is called a projection if x* = x = x 2. It is clear that both 1 and 0 are projections. For some C*-algebras 1 and 0 are the only projections. For example, if K is a connected compact Hausdorff space, C(K) does not have projections other than the constant functions 1 and 0. We show in this lecture that every von Neumann algebra possesses a lot of projections.
