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.
Acknowledgments
The authors are grateful to the reviewer for his/her kind comments and valuable suggestions, especially for English polishing, which greatly improved the readability and quality of the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).