The Spectral Shift Function and Spectral Flow
β Scribed by N. A. Azamov; A. L. Carey; F. A. Sukochev
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 377 KB
- Volume
- 276
- Category
- Article
- ISSN
- 0010-3616
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π SIMILAR VOLUMES
The new representation formula for the spectral shift function due to F. Gesztesy and K. A. Makarov is considered. This formula is extended to the case of relatively trace class perturbations. The proof is based on the analysis of a certain new unitary invariant for a pair of self-adjoint operators.
## Abstract We consider the threeβdimensional SchrΓΆdinger operator with constant magnetic field of strength __b__ > 0, and with smooth electric potential. The weak asymptotics of the spectral shift function with respect to __b__ β +β is studied. First, we fix the distance to the Landau levels, then
It is well known that the sum of negative (positive) eigenvalues of some finite Hermitian matrix V is concave (convex) with respect to V. Using the theory of the spectral shift function we generalize this property to self-adjoint operators on a separable Hilbert space with an arbitrary spectrum. Mor