On the pseudo-spectra and the related properties of infinite-dimensional Hamiltonian operators

Abstract

Given a linear operator T on a Hilbert space, the pseudo-point spectrum, the pseudo-residual spectrum, and the pseudo-continuous spectrum of T are defined, and some of their properties are studied. Furthermore, the structure of the pseudo-spectra of infinite-dimensional Hamiltonian operators is discussed, thus revealing their symmetry about the imaginary axis. Along the way, some examples are constructed to show the validity of our results.