We prove new spectral enclosures for the non-real spectrum of a class of 2×2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.
- block operator matrix
- quadratic numerical range
- spectral enclosure
- Gershgorin's circle
Giribet, J., Langer, M., Martínez Pería, F., Philipp, F., & Trunk, C. (2020). Spectral enclosures for a class of block operator matrices. Journal of Functional Analysis, 278(10), . https://doi.org/10.1016/j.jfa.2019.108455