Kaplansky density theorem

In the theory of von Neumann algebras, the Kaplansky density theorem, due to Irving Kaplansky, is a fundamental approximation theorem. The importance and ubiquity of this technical tool led Gert Pedersen to comment in one of his books[1] that,

The density theorem is Kaplansky's great gift to mankind. It can be used every day, and twice on Sundays.
  1. ^ Pg. 25; Pedersen, G. K., C*-algebras and their automorphism groups, London Mathematical Society Monographs, ISBN 978-0125494502.