We introduce and investigate the notion of a norming C*-subalgebra of C*-al
gebra. We characterize when von Neumann algebras norm B(H), and construct v
arious examples of abelian and hyperfinite norming subalgebras. We then app
ly these results to von Neumann algebra cohomology theory and the bounded p
rojection problem for von Neumann algebras. (C) 2000 Academic Press.