Publications Repository - Gdańsk University of Technology

We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell, Lee and Miller’s theorem a spectral flow formula for linear Hamiltonian systems which generalises a recent result of Hu and Portaluri.

Authors

• prof. dr hab. Marek Izydorek link open in new tab ,
• prof. dr hab. Joanna Janczewska link open in new tab ,
• Nils Waterstraat