Fredholm operators on C*-algebras
The aim of this note is to generalize the notion of Fredholm operator to an arbitrary C -algebra. Namely, we define “finite type” elements in an axiomatic way, and also we define a Fredholm type element a as such an element of a given C -algebra for which there are finite type elements p and q such...
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| További közreműködők: | |
| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2017
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| Sorozat: | Acta scientiarum mathematicarum
83 No. 3-4 |
| Kulcsszavak: | Algebra, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-015-526-5 |
| Online Access: | http://acta.bibl.u-szeged.hu/50054 |
| Tartalmi kivonat: | The aim of this note is to generalize the notion of Fredholm operator to an arbitrary C -algebra. Namely, we define “finite type” elements in an axiomatic way, and also we define a Fredholm type element a as such an element of a given C -algebra for which there are finite type elements p and q such that (1 − q)a(1 − p) is “invertible”. We derive an index theorem for such operators. In Applications we show that many well-known operators are special cases of our theory. Those include: classical Fredholm operators on a Hilbert space, Fredholm operators in the sense of Breuer, Atiyah and Singer on a properly infinite von Neumann algebra, and Fredholm operators on Hilbert C -modules over a unital C -algebra in the sense of Mishchenko and Fomenko. |
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| Terjedelem/Fizikai jellemzők: | 629-655 |
| ISSN: | 0001-6969 |