Kaydedildi:
| Yazar: | |
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| Materyal Türü: | Preprint |
| Baskı/Yayın Bilgisi: |
2000
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| Konular: | |
| Online Erişim: | https://arxiv.org/abs/math/0003185 |
| Etiketler: |
Etiketle
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| _version_ | 1866908353163165696 |
|---|---|
| author | Frank, Michael |
| author_facet | Frank, Michael |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0003185 |
| institution | arXiv |
| publishDate | 2000 |
| record_format | arxiv |
| spellingShingle | Hilbertian versus Hilbert W*-modules, and applications to $L^2$- and other invariants Frank, Michael Operator Algebras Differential Geometry Geometric Topology 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. |
| title | Hilbertian versus Hilbert W*-modules, and applications to $L^2$- and other invariants |
| topic | Operator Algebras Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/math/0003185 |