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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.

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