Mathematics – Functional Analysis
Scientific paper
2008-06-25
Mathematics
Functional Analysis
Final version to appear in Topological Methods in Nonlinear Analysis. 23 pages, LaTeX
Scientific paper
We give a definition of the spectral flow for paths of bounded essentially hyperbolic operators on a Banach space. The spectral flow induces a group homomorphism on the fundamental group of every connected component of the space of essentially hyperbolic operators. We prove that this homomorphism completes the exact homotopy sequence of a Serre fibration. This allows us to characterise its kernel and image and to produce examples of spaces where it is not injective or not surjective, unlike what happens for Hilbert spaces. For a large class of paths, namely the essentially splitting, the spectral flow of $ A $ coincides with $ -\ind(F_A) $, the Fredholm index of the differential operator $ F_A (u) = u' - A u $.
No associations
LandOfFree
On the spectral flow for paths of essentially hyperbolic bounded operators on Banach spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the spectral flow for paths of essentially hyperbolic bounded operators on Banach spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the spectral flow for paths of essentially hyperbolic bounded operators on Banach spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-162730