On Some Problems Studied by R. V. Kadison

Several problems studied by professor R. V. Kadison are shown to be closely related. The problems were originally formulated in the contexts of homomorphisms of C*-algebras, cohomology of von Neumann algebras and perturbations of C*-algebras. Recent research by G. Pisier has demonstrated that all of the problems considered are related to the question of whether all C*-algebras have finite length.