Block operator matrices and spectral decompositions

2017. 05. 10. 16:00
Nagy Béla (BME Matematika Intézet)

2x2 block operator matrices have been the subject of recent study in operator theory and also useful in some applications, e.g., for classes of differential operators. If the 4 operators forming the block are only closable or even closed linear operators in Banach or Hilbert spaces, then some unexpected difficulties arise that must be handled significantly more carefully than in the case of bounded entries. Sufficient conditions are known for the self-adjointness of the block operator or similarity to a self-adjoint operator, which play a useful role in the study of the so called supersymmetry phenomenon in quantum mechanics in connection with the Dirac operator. The arising spectral and generalized spectral measures will be useful also in the study of the structure of general closed linear operators in Hilbert space.