Spectra of 2×2 upper triangular operator matrices with unbounded entries
NGMEI QI, Deyu Wu, ATANCANG AL · Scientia Sinica Mathematica · 2016
In this paper, some properties of the spectrum, the approximate point spectrum, the detect spectrum and the essential spectrum of unbounded 2 2 upper triangular operator matrices with diagonal domain in Hilbert space are studied. Moreover, a necessary and sufficient condition under which the spectrum (resp. the approximate point spectrum, the detect spectrum) of operator matrices is equal to the union of the spectrum (resp. the approximate point spectrum, the detect spectrum) of diagonal entries is given. We also obtain a sufficient condition under which the essential spectrum of operator matrices is equal to the union of the essential spectrum of diagonal entries. In the end, the theory is applied to Hamiltonian operator matrix arising in mathematical physics.