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| Main Author: | |
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| Format: | Preprint |
| Published: |
2000
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0003185 |
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Table of Contents:
- 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 $C^*(π)$ of the fundamental group $π=π_1(M)$ of a manifold $M$). The results are of interest to specialists in operator algebras and global analysis.