According to the structure of characteristics of semi-Fredholm spectrum and Weyl spectrum of two given operators, the perturbation of Browder′s theorem (or Weyl′s theorem) for 2×2 upper triangular operator matrices with the two given operators as the main diagonal is researched. The sufficient and necessary condition for operator matrices satisfying the compact perturbation of Browder′s theorem (or Weyl′s theorem) are given.

Browder′s theorem; Weyl′s theorem; compact perturbation; spectrum