Hilbertian versus Hilbert W*-modules, and applications to $L^2$- and other invariants

Details Hilbertian versus Hilbert W*-modules, and applications to $L^2$- and other invariants Hilbertian versus Hilbert W*-modules, and applications to $L^2$- and other invariants

2000-03-28

arxiv.org/abs/math/0003185v2

Acta Appl. Math. 68(2001), 227-242

Mathematics

Operator Algebras

12 pages, Latex2e

Scientific paper

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.

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