The generalized Brauer–Ostrowski theorem for matrices of operators

Abstract

The classical Brauer–Ostrowski Theorem and the Ostrowski Theorem give spectral enclosures of matrices by a union of Cassini ovals and a union of some disks, respectively. In this paper, we obtain the corresponding results for operator matrices.

Keywords:

• Block operator matrices
• localization of the spectrum

2000 MR Subject Classifications:

• 47A10
• 47A05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Natural Science Foundation of China [12261065], Natural Science Foundation of Inner Mongolia [2021LHMS01004] and the Basic Science Research Fund in the Universities Directly under the InnerMongolia Autonomous Region [JY20220151].