Compact perturbations of both SVEP and Weyl's theorem for 3 × 3 upper triangular operator matrices

ABSTRACT

In this paper, we study the stability of Weyl's theorem and the stability of SVEP for $3\times 3$ upper triangular operator matrices, respectively. Also, we characterize the equivalent conditions when the stabilities of both Weyl's theorem and SVEP for $3\times 3$ upper triangular operator matrices hold at the same time.

COMMUNICATED BY:

• Ngai-Ching Wong

KEYWORDS:

• Weyl's theorem
• SVEP
• spectrum
• operator matrix

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11471200].