Hilbertian versus Hilbert W*-modules, and applications to $L^2$- and   other invariants
  Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The correspondence between these two structures sheds new light on basic results in $L^2$-invariant theory providing alternative proofs. We indicate new invariants for finitely generated projective B-modules, where B is supposed any unital C*-algebra, (usually the full group C*-algebra $C^*(\pi)$ of the fundamental group $\pi=\pi_1(M)$ of a manifold $M$). The results are of interest to specialists in operator algebras and global analysis. 
Michael Frank (University of Leipzig, Germany)