Semi-Fredholm theory in C*-algebras

Keckic and Lazovic introduced an axiomatic approach to Fredholm theory by introducing the notion of a Fredholm type element with respect to the ideal of finite type elements in a unital C*-algebra. This notion is a generalization of C*-Fredholm operator on the standard Hilbert C*-module introduced by Mishchenko and Fomenko and of Fredholm operator on a properly infinite von Neumann algebra introduced by Breuer. They obtained then that the set of Fredholm type elements in a unital C*-algebra is open in the norm topology and invariant under perturbation by finite type elements. Also, they proved multiplicativity of the index in the K-group and a generalization of the Atkinson theorem.
In this talk we shall present the results from semi-Fredholm theory in unital C*-algebras as a continuation of the approach by Keckic and Lazovic. We introduce the notion of a semi-Fredholm type element and semi-Weyl type element with respect to the ideal of finite type elements in a unital C*-algebra. We prove then the set of proper semi-Weyl elements is open in the norm topology, invariant under perturbations by finite type elements and several other results generalizing their counterparts from the classical semi-Fredholm theory of operators on Hilbert spaces. Also, we illustrate applications of our results to the special case of properly infinite von Neumann algebras. In particular, we obtain a generalization of punctured neighbourhood in this case and we describe the relationship between Fredholm spectra of 2 by 2 upper triangular matrices with coefficients in properly infinite von Neumann algebras and their diagonal entries.
Идентификатор конференции: 844 3430 3199 Код доступа: 991937