| Autor: |
Kečkić, Dragoljub J., Lazović, Zlatko |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Acta Sci. Math. (Szeged) 83 (2017), 629-655 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.14232/actasm-015-526-5 |
| Popis: |
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 Fredholm type element $a$ as such 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 index theorem for such operators. In applications we show that 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 an unital $C^*$-algebra in the sense of Mishchenko and Fomenko are special cases of our theory. |
| Databáze: |
arXiv |
| Externí odkaz: |
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