Winklmeier, Monika (Univ. of Bremen)

Off-Diagonalisation of a Certain Class of Block Operator Matrices

Scheduled for presentation during the Mini-Symposium "Block operator matrices and systems" (ThA13), Thursday, July 27, 2006, 10:25−10:50, Room 101

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

Block operator matrices V with domain D(V) = D_1 + D_2 in a Hilbert space H = H_1 + H_2 arise, e.g., in relativistic quantum mechanics.

Under the assumption that the offdiagonal entries of V are boundedly invertible and under some boundedness assumptions on the diagonal entries, we will show that the expression V-lambda allows a factorisation into three factors such that all the information about the spectrum of the block operatro matrix V is contained in a scalar operator valued function.

This factorisation is applied to the angular part of the Dirac operator in the Kerr-Newman background metric to obtain a lower bound for the modulus of the eigenvalues.